Edit Profile (opens in new tab) Jumarie, Guy M. Co-Author Distance Author ID: jumarie.guy-m Published as: Jumarie, Guy; Jumarie, G.; Jumarie, Guy M.; Zhyumari, Zh. more...less Documents Indexed: 251 Publications since 1969, including 4 Books 1 Further Contribution Reviewing Activity: 1,419 Reviews all top 5 Co-Authors 250 single-authored 1 Apter, H. 1 Atlan, Henri 1 Barthes, J. A. 1 Bertrand, Pierre 1 Boekee, Dick E. 1 Bourgois, M. 1 Caspi, Paul 1 Comyn, Gerard 1 Corfiati, L. 1 De Giacomo, P. 1 Dubuisson, Bernard 1 Dufour, Jacques 1 Evans, F. J. 1 Gilles, Gerard 1 Haken, Hermann 1 Hammad, Pierre 1 Hiroyuki, O. 1 Klir, George J. 1 Lafremiere, L. 1 Le Cardinal, Gilles 1 Le Guyader, Herve 1 Lefons, E. 1 Milgram, Maurice 1 Mili, Ali 1 Pagnotte, Yves 1 Pave, A. 1 Pazienza, Maria Teresa 1 Robach, Chantal 1 Schwarz, Jean-Jacques 1 Tangorra, F. 1 Vallée, Robert 1 Vallet, Claude 1 Vitry, G. 1 Vrison van Eck, W. F. V. 1 Walter, Eric all top 5 Serials 27 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 22 International Journal of Systems Science 19 Systems Analysis, Modelling Simulation 14 Chaos, Solitons and Fractals 14 Kybernetes 13 Annales des Télécommunications 12 Cybernetica 10 Cybernetics and Systems 7 Journal of Information & Optimization Sciences 7 Applied Mathematics Letters 7 Journal of Dynamic Systems, Measurement and Control 7 International Journal of Control, I. Series 6 Journal of the Franklin Institute 4 Journal of Mathematical Physics 4 Bulletin of the Calcutta Mathematical Society 4 Mathematical and Computer Modelling 4 Journal of Applied Mathematics and Computing 3 Computers & Mathematics with Applications 3 Journal of Optimization Theory and Applications 3 Insurance Mathematics & Economics 2 Information Sciences 2 Pattern Recognition Letters 2 Mathematical Engineering in Industry 1 Modern Physics Letters B 1 International Journal of Modern Physics A 1 International Journal of Control 1 International Journal of General Systems 1 Physica A 1 Physics Letters. A 1 Applied Mathematics and Computation 1 Fuzzy Sets and Systems 1 International Journal of Game Theory 1 Tamkang Journal of Mathematics 1 Utilitas Mathematica 1 Statistics & Probability Letters 1 Ricerche di Automatica 1 Mathematical Modelling 1 COMPEL 1 Revista de Matemáticas Aplicadas 1 International Journal of Electronics 1 Signal Processing 1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 1 Applied Mathematical Modelling 1 Automation and Remote Control 1 The Journal of Fuzzy Mathematics 1 Mathematical Modelling and Scientific Computing 1 Fractals 1 Review Bulletin of the Calcutta Mathematical Society 1 International Journal of Mathematics, Game Theory and Algebra 1 Acta Mathematica Sinica. English Series 1 Journal of Biological Systems 1 Physica Scripta 1 Nonlinear Analysis. Real World Applications 1 Nonlinear Analysis. Modelling and Control 1 Mathématiques et Sciences Humaines 1 International Journal of Evolution Equations 1 Revue du CETHEDEC 1 Fundamental Theories of Physics 1 Springer Series in Synergetics 1 Studies in Cybernetics 1 Applied Mathematical Sciences (Ruse) 1 Journal of Applied Mathematics & Informatics 1 Fractional Differential Calculus all top 5 Fields 99 Systems theory; control (93-XX) 93 Information and communication theory, circuits (94-XX) 68 Probability theory and stochastic processes (60-XX) 23 Computer science (68-XX) 22 Real functions (26-XX) 21 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 17 Partial differential equations (35-XX) 13 Statistics (62-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 11 Statistical mechanics, structure of matter (82-XX) 11 Biology and other natural sciences (92-XX) 10 Quantum theory (81-XX) 10 Relativity and gravitational theory (83-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Integral transforms, operational calculus (44-XX) 7 Measure and integration (28-XX) 6 Ordinary differential equations (34-XX) 6 Integral equations (45-XX) 6 Mechanics of particles and systems (70-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Mathematical logic and foundations (03-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Numerical analysis (65-XX) 4 Operations research, mathematical programming (90-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Functions of a complex variable (30-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Functional analysis (46-XX) 1 General and overarching topics; collections (00-XX) 1 Difference and functional equations (39-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 113 Publications have been cited 1,650 times in 907 Documents Cited by ▼ Year ▼ Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable. functions. Further results. Zbl 1137.65001 Jumarie, G. 348 2006 Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions. Zbl 1171.26305 Jumarie, Guy 160 2009 On the representation of fractional Brownian motion as an integral with respect to \((dt)^a\). Zbl 1082.60029 Jumarie, Guy 88 2005 Derivation and solutions of some fractional Black-Scholes equations in coarse-grained space and time. Application to Merton’s optimal portfolio. Zbl 1189.91230 Jumarie, Guy 85 2010 Laplace’s transform of fractional order via the Mittag-Leffler function and modified Riemann-Liouville derivative. Zbl 1181.44001 Jumarie, Guy 68 2009 New stochastic fractional models for Malthusian growth, the Poissonian birth process and optimal management of populations. Zbl 1130.92043 Jumarie, Guy 59 2006 Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution. Zbl 1145.26302 Jumarie, Guy 54 2007 On the solution of the stochastic differential equation of exponential growth driven by fractional Brownian motion. Zbl 1075.60068 Jumarie, Guy 52 2005 Stock exchange fractional dynamics defined as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional Black-Scholes equations. Zbl 1141.91455 Jumarie, Guy 50 2008 Cauchy’s integral formula via the modified Riemann-Liouville derivative for analytic functions of fractional order. Zbl 1202.30068 Jumarie, Guy 49 2010 Stochastic differential equations with fractional Brownian motion input. Zbl 0771.60043 Jumarie, Guy 48 1993 Lagrangian mechanics of fractional order, Hamilton-Jacobi fractional PDE and Taylor’s series of nondifferentiable functions. Zbl 1154.70011 Jumarie, Guy 35 2007 Fractional Brownian motions via random walk in the complex plane and via fractional derivative. Comparison and further results on their Fokker-Planck equations. Zbl 1068.60053 Jumarie, Guy 33 2004 Fractional master equation: Non-standard analysis and Liouville-Riemann derivative. Zbl 0994.82062 Jumarie, Guy 33 2001 An approach via fractional analysis to non-linearity induced by coarse-graining in space. Zbl 1195.37054 Jumarie, Guy 30 2010 A Fokker-Planck equation of fractional order with respect to time. Zbl 0761.60071 Jumarie, Guy 29 1992 Maximum entropy, information without probability and complex fractals. Classical and quantum approach. Zbl 0982.94001 Jumarie, Guy 25 2000 Fractional Hamilton-Jacobi equation for the optimal control of nonrandom fractional dynamics with fractional cost function. Zbl 1111.49014 Jumarie, Guy 21 2007 Schrödinger equation for quantum fractal space-time of order \(n\) via the complex-valued fractional Brownian motion. Zbl 1039.81008 Jumarie, Guy 19 2001 Modeling fractional stochastic systems as non-random fractional dynamics driven by Brownian motions. Zbl 1138.60324 Jumarie, Guy 17 2008 From Lagrangian mechanics fractal in space to space fractal Schrödinger’s equation via fractional Taylor’s series. Zbl 1198.70019 Jumarie, Guy 16 2009 Probability calculus of fractional order and fractional Taylor’s series application to Fokker-Planck equation and information of non-random functions. Zbl 1197.60039 Jumarie, Guy 14 2009 The Minkowski’s space-time is consistent with differential geometry of fractional order. Zbl 1197.83011 Jumarie, Guy 13 2007 New results on Fokker-Planck equations of fractional order. Zbl 1046.82515 Jumarie, Guy 13 2001 An approach to differential geometry of fractional order via modified Riemann-Liouville derivative. Zbl 1266.26013 Jumarie, Guy 13 2012 Relative information. Theories and applications. With forewords by G. J. Klir and H. Haken. Zbl 0719.94005 Jumarie, Guy 12 1990 Further advances on the general thermodynamics of open systems via information theory: Effective entropy, negative information. Zbl 0301.94033 Jumarie, Guy 11 1975 Merton’s model of optimal portfolio in a Black-Scholes market driven by a fractional Brownian motion with short-range dependence. Zbl 1104.91034 Jumarie, Guy 11 2005 A new approach to complex-valued fractional Brownian motion via rotating white noise. Zbl 0943.60086 Jumarie, Guy 9 1998 Information theory of deterministic functions. Some new applications to systems analysis. Zbl 0721.93004 Jumarie, G. 9 1990 A new approach to fractional Brownian motion of order \(n\) via random walk in the complex plane. Zbl 0973.60039 Jumarie, Guy 8 1999 Fractional Euler’s integral of first and second kinds. Application to fractional Hermite’s polynomials and to probability density of fractional order. Zbl 1234.26016 Jumarie, Guy 8 2010 Fractional multiple birth-death processes with birth probabilities \(\lambda _i(\Delta t)^\alpha +o((\Delta t)^\alpha)\). Zbl 1225.60141 Jumarie, Guy 8 2010 Derivation of an amplitude of information in the setting of a new family of fractional entropies. Zbl 1268.94017 Jumarie, Guy 8 2012 A practical variational approach to stochastic optimal control via state moment equations. Zbl 0855.93097 Jumarie, Guy 7 1995 A nonrandom variational approach to stochastic linear quadratic Gaussian optimization involving fractional noises (FLQG). Zbl 1106.49048 Jumarie, Guy 7 2005 Further results on the modelling of complex fractals in finance, scaling observation and optimal portfolio selection. Zbl 1092.91025 Jumarie, Guy 7 2002 Fractionalization of the complex-valued Brownian motion of order \(n\) using Riemann-Liouville derivative. Applications to mathematical finance and stochastic mechanics. Zbl 1099.60025 Jumarie, Guy 7 2006 Fractional Brownian motion with complex variance via random walk in the complex plane and applications. Zbl 0956.60031 Jumarie, Guy 6 2000 Solution of the multivariate Fokker-Planck equation by using a maximum path entropy principle. Zbl 0722.60085 Jumarie, Guy 5 1990 New results on the entropy of deterministic maps: Applications to Liapunov exponent, divergence, compositional inference, and pattern encoding. Zbl 0667.94004 Jumarie, Guy 5 1988 Stochastics of order \(n\) in biological systems. Applications to population dynamics, thermodynamics, nonequilibrium phase and complexity. Zbl 1041.92001 Jumarie, Guy 5 2003 From self-similarity to fractional derivative of non-differentiable functions via Mittag-Leffler function. Zbl 1175.26012 Jumarie, Guy 5 2008 Path integral for the probability of the trajectories generated by fractional dynamics subject to Gaussian white noise. Zbl 1142.82013 Jumarie, Guy 5 2007 Oscillation of nonlinear systems close to equilibrium position in the presence of coarse-graining in time and space. Zbl 1196.93030 Jumarie, G. 5 2009 Towards a new approach to self-organizing systems. Zbl 0268.93004 Jumarie, Guy 4 1973 A new approach to optimum state estimation in optimum system control. Zbl 0281.93016 Jumarie, G. 4 1975 On the fractional solution of the equation \(f(x+y)=f(x)f(y)\) and its application to fractional Laplace’s transform. Zbl 1291.26003 Jumarie, Guy 4 2012 Subjectivity, information, systems. An introduction to a theory of relativistic cybernetics. Transl. from the French, rev., expanded. Zbl 0623.94001 Jumarie, Guy M. 4 1986 A Minkowski theory of observation: Application to uncertainty and fuzziness. Zbl 0633.94007 Jumarie, Guy 4 1987 A theory of information for vague concepts. Outline of application to approximate reasoning. Zbl 0708.94006 Jumarie, Guy 4 1990 Simple general method to analyse the moment stability and sensitivity of nonlinear stochastic sytems with or without delay. Zbl 0641.93066 Jumarie, Guy 4 1988 A general paradigm for subjectivity in communication, subjective transinformation and subjective transuncertainty. Zbl 0478.94016 Jumarie, Guy 4 1981 A relativistic information theory model for general systems Lorentz transformation of organizability and structural entropy. Zbl 0311.94015 Jumarie, Guy 3 1975 Complex-valued Wiener measure: An approach via random walk in the complex plane. Zbl 0956.60028 Jumarie, Guy 3 1999 Informational entropy of distributed deterministic maps: applications to small samples of fuzzy sets and to pattern recognition. Zbl 0676.94006 Jumarie, Guy 3 1989 Extension of quantum information by using entropy of deterministic functions. Zbl 0752.94006 Jumarie, Guy 3 1991 Approximate solution for some stochastic differential equations involving both Gaussian and Poissonian white noises. Zbl 1049.60053 Jumarie, G. 3 2003 Further results on the information theory of deterministic functions and its application to pattern recognition. Zbl 0686.94004 Jumarie, Guy 3 1990 Renyi entropy of maps: Applications to fuzzy sets, pattern recognition, and chaotic dynamics. Zbl 0654.94006 Jumarie, Guy 3 1988 Subjective observation via informational invariance results in creation of fractals and self-similar processes of fractional order. Zbl 1225.93010 Jumarie, Guy 3 2010 The concept of structural entropy and its applications to general systems. Zbl 0409.93004 Jumarie, Guy 3 1979 On some similarities and differences between fractional probability density signed measure of probability and quantum probability. Zbl 1171.82320 Jumarie, Guy 3 2009 Generalization of the diffusion equation by using the maximum entropy principle. Zbl 0562.60087 Jumarie, Guy 3 1985 Path probability of random fractional systems defined by white noises in coarse-grained time. Application of fractional entropy. Zbl 1412.60059 Jumarie, Guy 3 2011 Riemann-Christoffel tensor in differential geometry of fractional order application to fractal space-time. Zbl 1302.35404 Jumarie, Guy 3 2013 A new information-theoretic approach to the entropy of non-random discrete maps relation to fractal dimension and temperature of curves. Zbl 0935.94008 Jumarie, Guy 2 1997 Input-output stability criteria for a broad class of stochastic nonlinear distributed systems defined by Green’s function. Zbl 0313.93064 Jumarie, G. 2 1975 Stock exchange dynamics involving both Gaussian and Poissonian white noises: Approximate solution via a symbolic stochastic calculus. Zbl 1055.91027 Jumarie, Guy 2 2002 Structural entropy, information potential, information balance and evolution in self-organizing systems. Zbl 0288.93003 Jumarie, Guy 2 1974 Tracking control of non-linear stochastic systems by using path cross- entropy and Fokker-Planck equation. Zbl 0761.93068 Jumarie, Guy 2 1992 On the effects of random time in dynamical systems. Zbl 1157.37327 Jumarie, Guy 2 2000 A practical approach to nonlinear estimation by using the maximum entropy principle. Zbl 0612.93062 Jumarie, Guy 2 1986 Improvement of stochastic neighbouring-optimal control using nonlinear Gaussian white noise terms in the Taylor expansions. Zbl 0887.93073 Jumarie, Guy 2 1996 Would dynamic systems involving human factors be necessarily of fractal nature? Zbl 1113.37316 Jumarie, Guy 2 2002 Théorie relativiste de l’information et telecommunication. Perspectives. Zbl 0382.94007 Jumarie, Guy 2 1978 An approach to encoding in the presence of subjectivity. Zbl 0466.94008 Jumarie, Guy 2 1980 Analysis of the equilibrium positions of nonlinear dynamical systems in the presence of coarse-graining disturbance in space. Zbl 1184.93067 Jumarie, Guy 2 2010 Mean-square criteria for the stability of non-linear distributed parameter systems. Zbl 0266.93043 Jumarie, Guy 1 1973 Possibility probability and relative information: A unified approach via geometric programming. Zbl 0935.94007 Jumarie, Guy 1 1995 Systems, catastrophe, chaos, synergetics. A unified approach via information of deterministic functions. Zbl 0673.94006 Jumarie, G. 1 1989 New approach to control and filtering of mechanical systems by using the estimates of their Lagrangians. Zbl 0697.93031 Jumarie, G. 1 1991 A practical criterion for the input-output stability of distributed parameter systems with space-dependent coefficients. Zbl 0296.93034 Jumarie, Guy 1 1975 Jeux différentiels structurels ou hyperjeux différentiels. Définition. Quelques propriétés. Perspectives. Zbl 0297.90119 Jumarie, Guy 1 1975 Information and quantum information of deterministic data with applications to systems analysis. Zbl 0763.94003 Jumarie, G. 1 1992 An approach to the entropy of (A or B) via maximization of conditional entropy. Zbl 0760.94002 Jumarie, Guy 1 1992 Further results on possibility-probability conversion via relative information and informational invariance. Zbl 0819.94015 Jumarie, Guy 1 1995 Quantum entropies of nonprobabilistic matrices. Zbl 0754.46051 Jumarie, Guy 1 1991 On some problems related to linear systems subject to squared white noises. Zbl 0521.60069 Jumarie, Guy 1 1983 A model of positive and negative information in the standard framework of communication theory - application to encoding. Zbl 0543.94004 Jumarie, Guy 1 1984 Entropy of fuzzy events revisited. An approach to fuzzy transinformation. Zbl 0524.94035 Jumarie, Guy 1 1983 Elements for a new information theory based on fractional calculus via modified Riemann-Liouville derivative. Zbl 1309.26008 Jumarie, Guy 1 2012 Total entropy. A unified approach to discrete entropy and continuous entropy. Zbl 0612.94005 Jumarie, Guy 1 1986 Mixed theories of information can be derived by using Shannon information only. Zbl 0612.94006 Jumarie, Guy 1 1986 Some approaches to the measure of the amount of information involved by a form. Zbl 0628.94008 Jumarie, G. 1 1986 Image processing. A new approach via informational entropy and informational divergence of non Random functions. Zbl 0866.68119 Jumarie, Guy 1 1996 Composition laws for entropy and temperature in tree-like graphs. Zbl 0791.94008 Jumarie, G. 1 1993 Entropy of Markovian processes: Application to image entropy in computer vision. Zbl 0994.94016 Jumarie, Guy 1 1998 Théorie relativiste de l’information. IV. Sur l’introduction de facteurs subjectifs dans les processus de communication. Zbl 0468.94002 Jumarie, Guy 1 1980 Sub-optimal control with observer of a two-lane highway traffic flow. Zbl 0464.93042 Jumarie, Guy 1 1981 Riemann-Christoffel tensor in differential geometry of fractional order application to fractal space-time. Zbl 1302.35404 Jumarie, Guy 3 2013 An approach to differential geometry of fractional order via modified Riemann-Liouville derivative. Zbl 1266.26013 Jumarie, Guy 13 2012 Derivation of an amplitude of information in the setting of a new family of fractional entropies. Zbl 1268.94017 Jumarie, Guy 8 2012 On the fractional solution of the equation \(f(x+y)=f(x)f(y)\) and its application to fractional Laplace’s transform. Zbl 1291.26003 Jumarie, Guy 4 2012 Elements for a new information theory based on fractional calculus via modified Riemann-Liouville derivative. Zbl 1309.26008 Jumarie, Guy 1 2012 Path probability of random fractional systems defined by white noises in coarse-grained time. Application of fractional entropy. Zbl 1412.60059 Jumarie, Guy 3 2011 Derivation and solutions of some fractional Black-Scholes equations in coarse-grained space and time. Application to Merton’s optimal portfolio. Zbl 1189.91230 Jumarie, Guy 85 2010 Cauchy’s integral formula via the modified Riemann-Liouville derivative for analytic functions of fractional order. Zbl 1202.30068 Jumarie, Guy 49 2010 An approach via fractional analysis to non-linearity induced by coarse-graining in space. Zbl 1195.37054 Jumarie, Guy 30 2010 Fractional Euler’s integral of first and second kinds. Application to fractional Hermite’s polynomials and to probability density of fractional order. Zbl 1234.26016 Jumarie, Guy 8 2010 Fractional multiple birth-death processes with birth probabilities \(\lambda _i(\Delta t)^\alpha +o((\Delta t)^\alpha)\). Zbl 1225.60141 Jumarie, Guy 8 2010 Subjective observation via informational invariance results in creation of fractals and self-similar processes of fractional order. Zbl 1225.93010 Jumarie, Guy 3 2010 Analysis of the equilibrium positions of nonlinear dynamical systems in the presence of coarse-graining disturbance in space. Zbl 1184.93067 Jumarie, Guy 2 2010 Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions. Zbl 1171.26305 Jumarie, Guy 160 2009 Laplace’s transform of fractional order via the Mittag-Leffler function and modified Riemann-Liouville derivative. Zbl 1181.44001 Jumarie, Guy 68 2009 From Lagrangian mechanics fractal in space to space fractal Schrödinger’s equation via fractional Taylor’s series. Zbl 1198.70019 Jumarie, Guy 16 2009 Probability calculus of fractional order and fractional Taylor’s series application to Fokker-Planck equation and information of non-random functions. Zbl 1197.60039 Jumarie, Guy 14 2009 Oscillation of nonlinear systems close to equilibrium position in the presence of coarse-graining in time and space. Zbl 1196.93030 Jumarie, G. 5 2009 On some similarities and differences between fractional probability density signed measure of probability and quantum probability. Zbl 1171.82320 Jumarie, Guy 3 2009 Stock exchange fractional dynamics defined as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional Black-Scholes equations. Zbl 1141.91455 Jumarie, Guy 50 2008 Modeling fractional stochastic systems as non-random fractional dynamics driven by Brownian motions. Zbl 1138.60324 Jumarie, Guy 17 2008 From self-similarity to fractional derivative of non-differentiable functions via Mittag-Leffler function. Zbl 1175.26012 Jumarie, Guy 5 2008 Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution. Zbl 1145.26302 Jumarie, Guy 54 2007 Lagrangian mechanics of fractional order, Hamilton-Jacobi fractional PDE and Taylor’s series of nondifferentiable functions. Zbl 1154.70011 Jumarie, Guy 35 2007 Fractional Hamilton-Jacobi equation for the optimal control of nonrandom fractional dynamics with fractional cost function. Zbl 1111.49014 Jumarie, Guy 21 2007 The Minkowski’s space-time is consistent with differential geometry of fractional order. Zbl 1197.83011 Jumarie, Guy 13 2007 Path integral for the probability of the trajectories generated by fractional dynamics subject to Gaussian white noise. Zbl 1142.82013 Jumarie, Guy 5 2007 Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable. functions. Further results. Zbl 1137.65001 Jumarie, G. 348 2006 New stochastic fractional models for Malthusian growth, the Poissonian birth process and optimal management of populations. Zbl 1130.92043 Jumarie, Guy 59 2006 Fractionalization of the complex-valued Brownian motion of order \(n\) using Riemann-Liouville derivative. Applications to mathematical finance and stochastic mechanics. Zbl 1099.60025 Jumarie, Guy 7 2006 Formal calculus for real-valued fractional Brownian motions prospects in systems science. Zbl 1160.93398 Jumarie, Guy 1 2006 On the representation of fractional Brownian motion as an integral with respect to \((dt)^a\). Zbl 1082.60029 Jumarie, Guy 88 2005 On the solution of the stochastic differential equation of exponential growth driven by fractional Brownian motion. Zbl 1075.60068 Jumarie, Guy 52 2005 Merton’s model of optimal portfolio in a Black-Scholes market driven by a fractional Brownian motion with short-range dependence. Zbl 1104.91034 Jumarie, Guy 11 2005 A nonrandom variational approach to stochastic linear quadratic Gaussian optimization involving fractional noises (FLQG). Zbl 1106.49048 Jumarie, Guy 7 2005 Fractional Brownian motions via random walk in the complex plane and via fractional derivative. Comparison and further results on their Fokker-Planck equations. Zbl 1068.60053 Jumarie, Guy 33 2004 Probability density of the complex-valued fractional Brownian motion of order \(n\) via the maximum entropy principle in \(\mathbb R_{+}^{1/n}\). Zbl 1061.60051 Jumarie, Guy 1 2004 Stochastics of order \(n\) in biological systems. Applications to population dynamics, thermodynamics, nonequilibrium phase and complexity. Zbl 1041.92001 Jumarie, Guy 5 2003 Approximate solution for some stochastic differential equations involving both Gaussian and Poissonian white noises. Zbl 1049.60053 Jumarie, G. 3 2003 Further results on the modelling of complex fractals in finance, scaling observation and optimal portfolio selection. Zbl 1092.91025 Jumarie, Guy 7 2002 Stock exchange dynamics involving both Gaussian and Poissonian white noises: Approximate solution via a symbolic stochastic calculus. Zbl 1055.91027 Jumarie, Guy 2 2002 Would dynamic systems involving human factors be necessarily of fractal nature? Zbl 1113.37316 Jumarie, Guy 2 2002 Fractional master equation: Non-standard analysis and Liouville-Riemann derivative. Zbl 0994.82062 Jumarie, Guy 33 2001 Schrödinger equation for quantum fractal space-time of order \(n\) via the complex-valued fractional Brownian motion. Zbl 1039.81008 Jumarie, Guy 19 2001 New results on Fokker-Planck equations of fractional order. Zbl 1046.82515 Jumarie, Guy 13 2001 Maximum entropy, information without probability and complex fractals. Classical and quantum approach. Zbl 0982.94001 Jumarie, Guy 25 2000 Fractional Brownian motion with complex variance via random walk in the complex plane and applications. Zbl 0956.60031 Jumarie, Guy 6 2000 On the effects of random time in dynamical systems. Zbl 1157.37327 Jumarie, Guy 2 2000 A new approach to fractional Brownian motion of order \(n\) via random walk in the complex plane. Zbl 0973.60039 Jumarie, Guy 8 1999 Complex-valued Wiener measure: An approach via random walk in the complex plane. Zbl 0956.60028 Jumarie, Guy 3 1999 A new approach to complex-valued fractional Brownian motion via rotating white noise. Zbl 0943.60086 Jumarie, Guy 9 1998 Entropy of Markovian processes: Application to image entropy in computer vision. Zbl 0994.94016 Jumarie, Guy 1 1998 A new information-theoretic approach to the entropy of non-random discrete maps relation to fractal dimension and temperature of curves. Zbl 0935.94008 Jumarie, Guy 2 1997 Improvement of stochastic neighbouring-optimal control using nonlinear Gaussian white noise terms in the Taylor expansions. Zbl 0887.93073 Jumarie, Guy 2 1996 Image processing. A new approach via informational entropy and informational divergence of non Random functions. Zbl 0866.68119 Jumarie, Guy 1 1996 A practical variational approach to stochastic optimal control via state moment equations. Zbl 0855.93097 Jumarie, Guy 7 1995 Possibility probability and relative information: A unified approach via geometric programming. Zbl 0935.94007 Jumarie, Guy 1 1995 Further results on possibility-probability conversion via relative information and informational invariance. Zbl 0819.94015 Jumarie, Guy 1 1995 Stochastic differential equations with fractional Brownian motion input. Zbl 0771.60043 Jumarie, Guy 48 1993 Composition laws for entropy and temperature in tree-like graphs. Zbl 0791.94008 Jumarie, G. 1 1993 A Fokker-Planck equation of fractional order with respect to time. Zbl 0761.60071 Jumarie, Guy 29 1992 Tracking control of non-linear stochastic systems by using path cross- entropy and Fokker-Planck equation. Zbl 0761.93068 Jumarie, Guy 2 1992 Information and quantum information of deterministic data with applications to systems analysis. Zbl 0763.94003 Jumarie, G. 1 1992 An approach to the entropy of (A or B) via maximization of conditional entropy. Zbl 0760.94002 Jumarie, Guy 1 1992 Extension of quantum information by using entropy of deterministic functions. Zbl 0752.94006 Jumarie, Guy 3 1991 New approach to control and filtering of mechanical systems by using the estimates of their Lagrangians. Zbl 0697.93031 Jumarie, G. 1 1991 Quantum entropies of nonprobabilistic matrices. Zbl 0754.46051 Jumarie, Guy 1 1991 Relative information. Theories and applications. With forewords by G. J. Klir and H. Haken. Zbl 0719.94005 Jumarie, Guy 12 1990 Information theory of deterministic functions. Some new applications to systems analysis. Zbl 0721.93004 Jumarie, G. 9 1990 Solution of the multivariate Fokker-Planck equation by using a maximum path entropy principle. Zbl 0722.60085 Jumarie, Guy 5 1990 A theory of information for vague concepts. Outline of application to approximate reasoning. Zbl 0708.94006 Jumarie, Guy 4 1990 Further results on the information theory of deterministic functions and its application to pattern recognition. Zbl 0686.94004 Jumarie, Guy 3 1990 An approach to the thermodynamic entropy and temperature of dynamic systems. Zbl 0709.94009 Jumarie, G. 1 1990 Informational entropy of distributed deterministic maps: applications to small samples of fuzzy sets and to pattern recognition. Zbl 0676.94006 Jumarie, Guy 3 1989 Systems, catastrophe, chaos, synergetics. A unified approach via information of deterministic functions. Zbl 0673.94006 Jumarie, G. 1 1989 New results on the entropy of deterministic maps: Applications to Liapunov exponent, divergence, compositional inference, and pattern encoding. Zbl 0667.94004 Jumarie, Guy 5 1988 Simple general method to analyse the moment stability and sensitivity of nonlinear stochastic sytems with or without delay. Zbl 0641.93066 Jumarie, Guy 4 1988 Renyi entropy of maps: Applications to fuzzy sets, pattern recognition, and chaotic dynamics. Zbl 0654.94006 Jumarie, Guy 3 1988 A Minkowski theory of observation: Application to uncertainty and fuzziness. Zbl 0633.94007 Jumarie, Guy 4 1987 Observation with informational invariance: Introduction to a new modeling of fuzzy arithmetics. Zbl 0636.94006 Jumarie, Guy 1 1987 Subjectivity, information, systems. An introduction to a theory of relativistic cybernetics. Transl. from the French, rev., expanded. Zbl 0623.94001 Jumarie, Guy M. 4 1986 A practical approach to nonlinear estimation by using the maximum entropy principle. Zbl 0612.93062 Jumarie, Guy 2 1986 Total entropy. A unified approach to discrete entropy and continuous entropy. Zbl 0612.94005 Jumarie, Guy 1 1986 Mixed theories of information can be derived by using Shannon information only. Zbl 0612.94006 Jumarie, Guy 1 1986 Some approaches to the measure of the amount of information involved by a form. Zbl 0628.94008 Jumarie, G. 1 1986 Generalization of the diffusion equation by using the maximum entropy principle. Zbl 0562.60087 Jumarie, Guy 3 1985 Stochastic processes with internal and external randomness. Modelling and analysis. Zbl 0581.60032 Jumarie, G. 1 1985 A model of positive and negative information in the standard framework of communication theory - application to encoding. Zbl 0543.94004 Jumarie, Guy 1 1984 Définition et applications d’une mesure de l’information tenant compte de la signification des symboles. (Definition and applications of an information measure which takes account of symbols and semantics). Zbl 0563.94007 Jumarie, Guy 1 1984 On some problems related to linear systems subject to squared white noises. Zbl 0521.60069 Jumarie, Guy 1 1983 Entropy of fuzzy events revisited. An approach to fuzzy transinformation. Zbl 0524.94035 Jumarie, Guy 1 1983 An approach, via entropy, to the stability of random large-scale sampled- data systems under structural perturbations. Zbl 0483.93086 Jumarie, Guy 1 1982 Théorie relativiste de l’information. V. Transfert d’information, transfert d’incertitude, bilan informationnel. Zbl 0486.94012 Jumarie, Guy 1 1982 A general paradigm for subjectivity in communication, subjective transinformation and subjective transuncertainty. Zbl 0478.94016 Jumarie, Guy 4 1981 Sub-optimal control with observer of a two-lane highway traffic flow. Zbl 0464.93042 Jumarie, Guy 1 1981 An approach to encoding in the presence of subjectivity. Zbl 0466.94008 Jumarie, Guy 2 1980 Théorie relativiste de l’information. IV. Sur l’introduction de facteurs subjectifs dans les processus de communication. Zbl 0468.94002 Jumarie, Guy 1 1980 Subjectivite, information, système. Synthese pour une cybernetique relativiste. Zbl 0441.94005 Jumarie, Guy 1 1980 The concept of structural entropy and its applications to general systems. Zbl 0409.93004 Jumarie, Guy 3 1979 New results in relativistic information and general systems. Renyi entropy, observed probability, relativistic fuzzy sets, generative semantics. Zbl 0412.94013 Jumarie, Guy 1 1979 ...and 13 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,406 Authors 90 Jumarie, Guy M. 16 Băleanu, Dumitru I. 15 Bekir, Ahmet 13 Güner, Özkan 13 Yang, Xiao-Jun 11 Atangana, Abdon 8 Kiliçman, Adem 8 Ren, Fuyao 7 Ezzat, Magdy A. 7 Inc, Mustafa 7 Liu, Fawang 7 Ostoja-Starzewski, Martin 7 Qiu, Weiyuan 7 Torres, Delfim Fernando Marado 6 Abdel-Salam, Emad A-B. 6 He, Ji-Huan 6 Liang, Jinrong 6 Machado, José António Tenreiro 6 Roul, Pradip 6 Rui, Weiguo 6 Zheng, Bin 5 Almeida, Ricardo 5 Cevikel, Adem Cengiz 5 Dai, Chaoqing 5 Feng, Qinghua 5 Ghosh, Uttam 5 Ilhan, Onur Alp 5 Malinowska, Agnieszka Barbara 5 Mohyud-Din, Syed Tauseef 5 Ordokhani, Yadollah 5 Pandir, Yusuf 5 Saha Ray, Santanu 5 Srivastava, Hari Mohan 5 Tian, Shoufu 5 Wang, Xiaotian 5 Wu, Guocheng 5 Yang, Hongwei 5 Zhang, Yi 4 Abdou, Mohamed Aly Mohamed 4 Ahmad, Jamshad 4 Akgül, Ali 4 Ali Akbar, M. 4 Anwar, Muhammad Shoaib 4 Beghin, Luisa 4 Cahoy, Dexter O. 4 El-Karamany, Ahmed S. 4 Gómez-Aguilar, José Francisco 4 Guo, Shimin 4 Lashkarian, Elham 4 Li, Chao 4 Li, Jun 4 Li, Zhengbiao 4 Liu, Chengshi 4 Manafian Heris, Jalil 4 Mei, Liquan 4 Mirzazadeh, Mohammad 4 Misirli, Emine E. 4 Qin, Chunyan 4 Rasheed, Amer 4 Sahoo, Subhadarshan 4 Sarkar, Susmita 4 Song, Lina 4 Trujillo, Juan J. 4 Turner, Ian William 4 Usman, Muhammad 4 Vuković, Predrag D. 4 Wang, Xiubin 4 Wang, Yueyue 4 Wu, Jianglun 4 Zhang, Tiantian 3 Abouagwa, Mahmoud 3 Abouelregal, Ahmed E. 3 Ahmed, Naveed 3 Aksoy, Esin 3 Ali, Khalid Karam 3 Aliyu, Aliyu Isa 3 Anh, Vo V. 3 Aslan, İsmail 3 Awonusika, Richard Olu 3 Bagyalakshmi, Morachan 3 Balachandran, Krishnan 3 Balyan, Lokendra K. 3 Baskonus, Haci Mehmet 3 Choi, Jin Hyuk 3 Coloma, Nicolás 3 Das, Amiya 3 Das, Shantanu 3 de Oliveira, Edmundo Capelas 3 Debbouche, Amar 3 Demmie, Paul N. 3 El-Nabulsi, Rami Ahmad 3 Faraz, Naeem 3 Gideon, Frednard 3 Golbabai, Ahmad 3 Golmankhaneh, Alireza Khalili 3 Guo, Qilong 3 Ibrahim, Rabha Waell 3 Islam, Md. Nurul 3 Jafari, Hossein 3 Joumaa, Hady ...and 1,306 more Authors all top 5 Cited in 222 Serials 50 Chaos, Solitons and Fractals 36 Mathematical Methods in the Applied Sciences 31 Advances in Difference Equations 30 Computers & Mathematics with Applications 27 Abstract and Applied Analysis 25 Communications in Nonlinear Science and Numerical Simulation 23 Applied Mathematics Letters 23 Mathematical Problems in Engineering 22 Physica A 21 Physics Letters. 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Transaction A: Science 2 Analysis and Applications (Singapore) 2 Stochastics ...and 122 more Serials all top 5 Cited in 46 Fields 388 Partial differential equations (35-XX) 254 Real functions (26-XX) 164 Ordinary differential equations (34-XX) 155 Numerical analysis (65-XX) 131 Probability theory and stochastic processes (60-XX) 88 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 65 Systems theory; control (93-XX) 51 Information and communication theory, circuits (94-XX) 50 Statistical mechanics, structure of matter (82-XX) 44 Dynamical systems and ergodic theory (37-XX) 40 Mechanics of deformable solids (74-XX) 38 Biology and other natural sciences (92-XX) 36 Fluid mechanics (76-XX) 35 Special functions (33-XX) 29 Measure and integration (28-XX) 29 Integral transforms, operational calculus (44-XX) 29 Integral equations (45-XX) 29 Calculus of variations and optimal control; optimization (49-XX) 22 Statistics (62-XX) 21 Computer science (68-XX) 17 Mechanics of particles and systems (70-XX) 17 Classical thermodynamics, heat transfer (80-XX) 16 Quantum theory (81-XX) 15 Difference and functional equations (39-XX) 13 Operator theory (47-XX) 12 Operations research, mathematical programming (90-XX) 10 Functions of a complex variable (30-XX) 8 Relativity and gravitational theory (83-XX) 7 Optics, electromagnetic theory (78-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Topological groups, Lie groups (22-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Functional analysis (46-XX) 5 Differential geometry (53-XX) 5 Geophysics (86-XX) 4 Approximations and expansions (41-XX) 3 Combinatorics (05-XX) 2 Mathematical logic and foundations (03-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Sequences, series, summability (40-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 General topology (54-XX) Citations by Year