Srivastava, H. M.; Mandal, H.; Bira, B. Lie symmetry and exact solution of the time-fractional Hirota-Satsuma Korteweg-de Vries system. (English) Zbl 1477.35227 Russ. J. Math. Phys. 28, No. 3, 284-292 (2021). MSC: 35Q53 22E70 26A33 35R11 35R03 PDFBibTeX XMLCite \textit{H. M. Srivastava} et al., Russ. J. Math. Phys. 28, No. 3, 284--292 (2021; Zbl 1477.35227) Full Text: DOI
Redhwan, Saleh S.; Shaikh, Sadikali L.; Abdo, Mohammed S. Implicit fractional differential equation with anti-periodic boundary condition involving Caputo-Katugampola type. (English) Zbl 1484.34075 AIMS Math. 5, No. 4, 3714-3730 (2020). MSC: 34B15 34B18 26A33 34A12 PDFBibTeX XMLCite \textit{S. S. Redhwan} et al., AIMS Math. 5, No. 4, 3714--3730 (2020; Zbl 1484.34075) Full Text: DOI
Sheng, Yuhong; Yao, Kai; Qin, Zhongfeng Continuity and variation analysis of fractional uncertain processes. (English) Zbl 1495.60020 Chaos Solitons Fractals 140, Article ID 110250, 6 p. (2020). MSC: 60G18 94A17 PDFBibTeX XMLCite \textit{Y. Sheng} et al., Chaos Solitons Fractals 140, Article ID 110250, 6 p. (2020; Zbl 1495.60020) Full Text: DOI
Fischer, C.; Zourmba, K.; Mohamadou, A. Lyapunov exponents spectrum estimation of fractional order nonlinear systems using cloned dynamics. (English) Zbl 1437.65058 Appl. Numer. Math. 154, 187-204 (2020). MSC: 65L03 65P20 37M99 26A33 34A08 37D45 PDFBibTeX XMLCite \textit{C. Fischer} et al., Appl. Numer. Math. 154, 187--204 (2020; Zbl 1437.65058) Full Text: DOI
Alharbi, Fahad M.; Baleanu, Dumitru; Ebaid, Abdelhalim Physical properties of the projectile motion using the conformable derivative. (English) Zbl 07822227 Chin. J. Phys., Taipei 58, 18-28 (2019). MSC: 26Axx PDFBibTeX XMLCite \textit{F. M. Alharbi} et al., Chin. J. Phys., Taipei 58, 18--28 (2019; Zbl 07822227) Full Text: DOI
Jin, Ting; Sun, Yun; Zhu, Yuanguo Extreme values for solution to uncertain fractional differential equation and application to American option pricing model. (English) Zbl 07570718 Physica A 534, Article ID 122357, 13 p. (2019). MSC: 82-XX PDFBibTeX XMLCite \textit{T. Jin} et al., Physica A 534, Article ID 122357, 13 p. (2019; Zbl 07570718) Full Text: DOI
Maitama, Shehu; Zhao, Weidong Local fractional Laplace homotopy analysis method for solving non-differentiable wave equations on Cantor sets. (English) Zbl 1463.65339 Comput. Appl. Math. 38, No. 2, Paper No. 65, 22 p. (2019). MSC: 65M99 26A33 35R11 68W30 PDFBibTeX XMLCite \textit{S. Maitama} and \textit{W. Zhao}, Comput. Appl. Math. 38, No. 2, Paper No. 65, 22 p. (2019; Zbl 1463.65339) Full Text: DOI
Tapiero, Charles S.; Vallois, Pierre Fractional randomness and the Brownian bridge. (English) Zbl 1514.60050 Physica A 503, 835-843 (2018). MSC: 60G22 26A33 PDFBibTeX XMLCite \textit{C. S. Tapiero} and \textit{P. Vallois}, Physica A 503, 835--843 (2018; Zbl 1514.60050) Full Text: DOI
Liu, Cheng-shi Counterexamples on Jumarie’s three basic fractional calculus formulae for non-differentiable continuous functions. (English) Zbl 1390.26011 Chaos Solitons Fractals 109, 219-222 (2018). MSC: 26A33 PDFBibTeX XMLCite \textit{C.-s. Liu}, Chaos Solitons Fractals 109, 219--222 (2018; Zbl 1390.26011) Full Text: DOI arXiv
Wu, Qiong A new type of the Gronwall-Bellman inequality and its application to fractional stochastic differential equations. (English) Zbl 1438.26105 Cogent Math. 4, Article ID 1279781, 13 p. (2017). MSC: 26D15 26A33 60H10 PDFBibTeX XMLCite \textit{Q. Wu}, Cogent Math. 4, Article ID 1279781, 13 p. (2017; Zbl 1438.26105) Full Text: DOI arXiv
Guo, Yingjia The stability of the positive solution for a fractional SIR model. (English) Zbl 1366.92123 Int. J. Biomath. 10, No. 1, Article ID 1750014, 14 p. (2017). MSC: 92D30 34A08 34D20 PDFBibTeX XMLCite \textit{Y. Guo}, Int. J. Biomath. 10, No. 1, Article ID 1750014, 14 p. (2017; Zbl 1366.92123) Full Text: DOI
Tapiero, Charles S.; Vallois, Pierre Fractional randomness. (English) Zbl 1400.60020 Physica A 462, 1161-1177 (2016). MSC: 60E05 26A33 PDFBibTeX XMLCite \textit{C. S. Tapiero} and \textit{P. Vallois}, Physica A 462, 1161--1177 (2016; Zbl 1400.60020) Full Text: DOI
Atangana, Abdon; Baleanu, Dumitru; Al Qurashi, Maysaa’ Mohamed; Yang, Xiao-Jun On the nonlinear perturbation \(K(n, m)\) Rosenau-Hyman equation: a model of nonlinear scattering wave. (English) Zbl 1375.35441 Adv. Math. Phys. 2015, Article ID 746327, 8 p. (2015). MSC: 35Q53 35Q35 35R11 76B15 76D33 PDFBibTeX XMLCite \textit{A. Atangana} et al., Adv. Math. Phys. 2015, Article ID 746327, 8 p. (2015; Zbl 1375.35441) Full Text: DOI
Liu, Cheng-shi Counterexamples on Jumarie’s two basic fractional calculus formulae. (English) Zbl 1331.26010 Commun. Nonlinear Sci. Numer. Simul. 22, No. 1-3, 92-94 (2015). MSC: 26A33 PDFBibTeX XMLCite \textit{C.-s. Liu}, Commun. Nonlinear Sci. Numer. Simul. 22, No. 1--3, 92--94 (2015; Zbl 1331.26010) Full Text: DOI
Li, Qing; Zhou, Yanli; Zhao, Xinquan; Ge, Xiangyu Fractional order stochastic differential equation with application in European option pricing. (English) Zbl 1419.34029 Discrete Dyn. Nat. Soc. 2014, Article ID 621895, 12 p. (2014). MSC: 34A08 91G20 60H10 PDFBibTeX XMLCite \textit{Q. Li} et al., Discrete Dyn. Nat. Soc. 2014, Article ID 621895, 12 p. (2014; Zbl 1419.34029) Full Text: DOI
de Oliveira, Edmundo Capelas; Tenreiro Machado, José António A review of definitions for fractional derivatives and integral. (English) Zbl 1407.26013 Math. Probl. Eng. 2014, Article ID 238459, 6 p. (2014). MSC: 26A33 PDFBibTeX XMLCite \textit{E. C. de Oliveira} and \textit{J. A. Tenreiro Machado}, Math. Probl. Eng. 2014, Article ID 238459, 6 p. (2014; Zbl 1407.26013) Full Text: DOI
Gaur, M.; Singh, Karan On group invariant solutions of fractional order Burgers-Poisson equation. (English) Zbl 1335.35276 Appl. Math. Comput. 244, 870-877 (2014). MSC: 35R11 35Q53 PDFBibTeX XMLCite \textit{M. Gaur} and \textit{K. Singh}, Appl. Math. Comput. 244, 870--877 (2014; Zbl 1335.35276) Full Text: DOI
Merdan, Mehmet On the solutions of nonlinear fractional Klein-Gordon equation with modified Riemann-Liouville derivative. (English) Zbl 1334.35393 Appl. Math. Comput. 242, 877-888 (2014). MSC: 35R11 35C05 35Q53 PDFBibTeX XMLCite \textit{M. Merdan}, Appl. Math. Comput. 242, 877--888 (2014; Zbl 1334.35393) Full Text: DOI
Stern, Robin; Effenberger, Frederic; Fichtner, Horst; Schäfer, Tobias The space-fractional diffusion-advection equation: analytical solutions and critical assessment of numerical solutions. (English) Zbl 1312.35188 Fract. Calc. Appl. Anal. 17, No. 1, 171-190 (2014). MSC: 35R11 33C60 60J60 65C05 65M06 35R60 PDFBibTeX XMLCite \textit{R. Stern} et al., Fract. Calc. Appl. Anal. 17, No. 1, 171--190 (2014; Zbl 1312.35188) Full Text: DOI arXiv
Xu, Yong; Guo, Rong; Liu, Di; Zhang, Huiqing; Duan, Jinqiao Stochastic averaging principle for dynamical systems with fractional Brownian motion. (English) Zbl 1314.60122 Discrete Contin. Dyn. Syst., Ser. B 19, No. 4, 1197-1212 (2014). MSC: 60H10 60G22 60H05 34F05 37H10 93E03 PDFBibTeX XMLCite \textit{Y. Xu} et al., Discrete Contin. Dyn. Syst., Ser. B 19, No. 4, 1197--1212 (2014; Zbl 1314.60122) Full Text: DOI arXiv
Atangana, Abdon; Ahmed, O. Aden; Bıldık, Necdet A generalized version of a low velocity impact between a rigid sphere and a transversely isotropic strain-hardening plate supported by a rigid substrate using the concept of noninteger derivatives. (English) Zbl 1364.74039 Abstr. Appl. Anal. 2013, Article ID 671321, 9 p. (2013). MSC: 74G10 74M15 26A33 35R11 74K20 PDFBibTeX XMLCite \textit{A. Atangana} et al., Abstr. Appl. Anal. 2013, Article ID 671321, 9 p. (2013; Zbl 1364.74039) Full Text: DOI
Atangana, Abdon; Secer, Aydin A note on fractional order derivatives and table of fractional derivatives of some special functions. (English) Zbl 1276.26010 Abstr. Appl. Anal. 2013, Article ID 279681, 8 p. (2013). MSC: 26A33 PDFBibTeX XMLCite \textit{A. Atangana} and \textit{A. Secer}, Abstr. Appl. Anal. 2013, Article ID 279681, 8 p. (2013; Zbl 1276.26010) Full Text: DOI
Jumarie, Guy Riemann-Christoffel tensor in differential geometry of fractional order application to fractal space-time. (English) Zbl 1302.35404 Fractals 21, No. 1, Article ID 1350004, 27 p. (2013). MSC: 35R11 53B20 26A33 PDFBibTeX XMLCite \textit{G. Jumarie}, Fractals 21, No. 1, Article ID 1350004, 27 p. (2013; Zbl 1302.35404) Full Text: DOI
Yin, Fukang; Song, Junqiang; Cao, Xiaoqun A general iteration formula of VIM for fractional heat- and wave-like equations. (English) Zbl 1266.35142 J. Appl. Math. 2013, Article ID 428079, 9 p. (2013). MSC: 35R11 35A15 PDFBibTeX XMLCite \textit{F. Yin} et al., J. Appl. Math. 2013, Article ID 428079, 9 p. (2013; Zbl 1266.35142) Full Text: DOI
Jumarie, Guy On the fractional solution of the equation \(f(x+y)=f(x)f(y)\) and its application to fractional Laplace’s transform. (English) Zbl 1291.26003 Appl. Math. Comput. 219, No. 4, 1625-1643 (2012). MSC: 26A33 PDFBibTeX XMLCite \textit{G. Jumarie}, Appl. Math. Comput. 219, No. 4, 1625--1643 (2012; Zbl 1291.26003) Full Text: DOI
Pedjeu, Jean-C.; Ladde, Gangaram S. Stochastic fractional differential equations: modeling, method and analysis. (English) Zbl 1282.60058 Chaos Solitons Fractals 45, No. 3, 279-293 (2012). Reviewer: Maria Stolarczyk (Katowice) MSC: 60H10 60H05 60G22 37A50 PDFBibTeX XMLCite \textit{J.-C. Pedjeu} and \textit{G. S. Ladde}, Chaos Solitons Fractals 45, No. 3, 279--293 (2012; Zbl 1282.60058) Full Text: DOI Link
Jumarie, Guy An approach to differential geometry of fractional order via modified Riemann-Liouville derivative. (English) Zbl 1266.26013 Acta Math. Sin., Engl. Ser. 28, No. 9, 1741-1768 (2012). MSC: 26A33 PDFBibTeX XMLCite \textit{G. Jumarie}, Acta Math. Sin., Engl. Ser. 28, No. 9, 1741--1768 (2012; Zbl 1266.26013) Full Text: DOI
Jumarie, Guy Derivation of an amplitude of information in the setting of a new family of fractional entropies. (English) Zbl 1268.94017 Inf. Sci. 216, 113-137 (2012). Reviewer: Pushpa N. Rathie (Brasilia) MSC: 94A17 26A33 39B05 94D05 PDFBibTeX XMLCite \textit{G. Jumarie}, Inf. Sci. 216, 113--137 (2012; Zbl 1268.94017) Full Text: DOI
Merdan, Mehmet On the solutions fractional Riccati differential equation with modified Riemann-Liouville derivative. (English) Zbl 1251.34011 Int. J. Differ. Equ. 2012, Article ID 346089, 17 p. (2012). MSC: 34A08 34A25 34A45 34A12 PDFBibTeX XMLCite \textit{M. Merdan}, Int. J. Differ. Equ. 2012, Article ID 346089, 17 p. (2012; Zbl 1251.34011) Full Text: DOI
Liang, Jin-Rong; Wang, Jun; Lǔ, Long-Jin; Gu, Hui; Qiu, Wei-Yuan; Ren, Fu-Yao Fractional Fokker-Planck equation and Black-Scholes formula in composite-diffusive regime. (English) Zbl 1245.82054 J. Stat. Phys. 146, No. 1, 205-216 (2012). Reviewer: Bassano Vacchini (Milano) MSC: 82C31 35R11 35Q84 35Q91 PDFBibTeX XMLCite \textit{J.-R. Liang} et al., J. Stat. Phys. 146, No. 1, 205--216 (2012; Zbl 1245.82054) Full Text: DOI
Jumarie, Guy Path probability of random fractional systems defined by white noises in coarse-grained time. Application of fractional entropy. (English) Zbl 1412.60059 Fract. Differ. Calc. 1, No. 1, 45-87 (2011). MSC: 60G22 60J65 26A33 PDFBibTeX XMLCite \textit{G. Jumarie}, Fract. Differ. Calc. 1, No. 1, 45--87 (2011; Zbl 1412.60059) Full Text: DOI
Jumarie, Guy Fractional multiple birth-death processes with birth probabilities \(\lambda _i(\Delta t)^\alpha +o((\Delta t)^\alpha)\). (English) Zbl 1225.60141 J. Franklin Inst. 347, No. 10, 1797-1813 (2010). Reviewer: Matthias Meiners (Münster) MSC: 60J80 60J27 26A33 34A08 92D25 PDFBibTeX XMLCite \textit{G. Jumarie}, J. Franklin Inst. 347, No. 10, 1797--1813 (2010; Zbl 1225.60141) Full Text: DOI
Jumarie, Guy Cauchy’s integral formula via the modified Riemann-Liouville derivative for analytic functions of fractional order. (English) Zbl 1202.30068 Appl. Math. Lett. 23, No. 12, 1444-1450 (2010). MSC: 30E99 26A33 PDFBibTeX XMLCite \textit{G. Jumarie}, Appl. Math. Lett. 23, No. 12, 1444--1450 (2010; Zbl 1202.30068) Full Text: DOI
Jumarie, Guy Derivation and solutions of some fractional Black-Scholes equations in coarse-grained space and time. Application to Merton’s optimal portfolio. (English) Zbl 1189.91230 Comput. Math. Appl. 59, No. 3, 1142-1164 (2010). MSC: 91G80 26A33 35R11 45K05 PDFBibTeX XMLCite \textit{G. Jumarie}, Comput. Math. Appl. 59, No. 3, 1142--1164 (2010; Zbl 1189.91230) Full Text: DOI
Jumarie, Guy Analysis of the equilibrium positions of nonlinear dynamical systems in the presence of coarse-graining disturbance in space. (English) Zbl 1184.93067 J. Appl. Math. Comput. 32, No. 2, 329-351 (2010). MSC: 93C10 26A33 60J65 93B18 93D30 PDFBibTeX XMLCite \textit{G. Jumarie}, J. Appl. Math. Comput. 32, No. 2, 329--351 (2010; Zbl 1184.93067) Full Text: DOI
Jumarie, Guy An approach via fractional analysis to non-linearity induced by coarse-graining in space. (English) Zbl 1195.37054 Nonlinear Anal., Real World Appl. 11, No. 1, 535-546 (2010). Reviewer: Fuhua Ling (Milpitas) MSC: 37L99 60J65 60H40 PDFBibTeX XMLCite \textit{G. Jumarie}, Nonlinear Anal., Real World Appl. 11, No. 1, 535--546 (2010; Zbl 1195.37054) Full Text: DOI
Jumarie, Guy From Lagrangian mechanics fractal in space to space fractal Schrödinger’s equation via fractional Taylor’s series. (English) Zbl 1198.70019 Chaos Solitons Fractals 41, No. 4, 1590-1604 (2009). MSC: 70S05 81Q65 26A33 PDFBibTeX XMLCite \textit{G. Jumarie}, Chaos Solitons Fractals 41, No. 4, 1590--1604 (2009; Zbl 1198.70019) Full Text: DOI
Jumarie, Guy Probability calculus of fractional order and fractional Taylor’s series application to Fokker-Planck equation and information of non-random functions. (English) Zbl 1197.60039 Chaos Solitons Fractals 40, No. 3, 1428-1448 (2009). MSC: 60G18 35Q84 26A33 60J60 82C31 94A15 PDFBibTeX XMLCite \textit{G. Jumarie}, Chaos Solitons Fractals 40, No. 3, 1428--1448 (2009; Zbl 1197.60039) Full Text: DOI
Jumarie, Guy Laplace’s transform of fractional order via the Mittag-Leffler function and modified Riemann-Liouville derivative. (English) Zbl 1181.44001 Appl. Math. Lett. 22, No. 11, 1659-1664 (2009). Reviewer: Lothar Berg (Rostock) MSC: 44A10 44A20 26A33 33E12 PDFBibTeX XMLCite \textit{G. Jumarie}, Appl. Math. Lett. 22, No. 11, 1659--1664 (2009; Zbl 1181.44001) Full Text: DOI
Jumarie, Guy Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions. (English) Zbl 1171.26305 Appl. Math. Lett. 22, No. 3, 378-385 (2009). Reviewer: Tej Singh Nahar (Bhilwara) MSC: 26A33 PDFBibTeX XMLCite \textit{G. Jumarie}, Appl. Math. Lett. 22, No. 3, 378--385 (2009; Zbl 1171.26305) Full Text: DOI
Jumarie, Guy Stock exchange fractional dynamics defined as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional Black-Scholes equations. (English) Zbl 1141.91455 Insur. Math. Econ. 42, No. 1, 271-287 (2008). MSC: 91B28 91B62 PDFBibTeX XMLCite \textit{G. Jumarie}, Insur. Math. Econ. 42, No. 1, 271--287 (2008; Zbl 1141.91455) Full Text: DOI
Jumarie, Guy Modeling fractional stochastic systems as non-random fractional dynamics driven by Brownian motions. (English) Zbl 1138.60324 Appl. Math. Modelling 32, No. 5, 836-859 (2008). MSC: 60H10 60G15 34F05 PDFBibTeX XMLCite \textit{G. Jumarie}, Appl. Math. Modelling 32, No. 5, 836--859 (2008; Zbl 1138.60324) Full Text: DOI
Jumarie, Guy Path integral for the probability of the trajectories generated by fractional dynamics subject to Gaussian white noise. (English) Zbl 1142.82013 Appl. Math. Lett. 20, No. 8, 846-852 (2007). Reviewer: Bassano Vacchini (Milano) MSC: 82C31 26A33 PDFBibTeX XMLCite \textit{G. Jumarie}, Appl. Math. Lett. 20, No. 8, 846--852 (2007; Zbl 1142.82013) Full Text: DOI
Jumarie, Guy Lagrangian mechanics of fractional order, Hamilton-Jacobi fractional PDE and Taylor’s series of nondifferentiable functions. (English) Zbl 1154.70011 Chaos Solitons Fractals 32, No. 3, 969-987 (2007). MSC: 70Q05 70H03 70H20 26A33 PDFBibTeX XMLCite \textit{G. Jumarie}, Chaos Solitons Fractals 32, No. 3, 969--987 (2007; Zbl 1154.70011) Full Text: DOI
Jumarie, Guy Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution. (English) Zbl 1145.26302 J. Appl. Math. Comput. 24, No. 1-2, 31-48 (2007). Reviewer: Stefan G. Samko (Faro) MSC: 26A33 49K20 44A10 PDFBibTeX XMLCite \textit{G. Jumarie}, J. Appl. Math. Comput. 24, No. 1--2, 31--48 (2007; Zbl 1145.26302) Full Text: DOI
Jumarie, Guy Fractional Hamilton-Jacobi equation for the optimal control of nonrandom fractional dynamics with fractional cost function. (English) Zbl 1111.49014 J. Appl. Math. Comput. 23, No. 1-2, 215-228 (2007). MSC: 49K15 90C39 60G18 49L20 49K20 PDFBibTeX XMLCite \textit{G. Jumarie}, J. Appl. Math. Comput. 23, No. 1--2, 215--228 (2007; Zbl 1111.49014) Full Text: DOI
Jumarie, G. Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable. functions. Further results. (English) Zbl 1137.65001 Comput. Math. Appl. 51, No. 9-10, 1367-1376 (2006). MSC: 65B15 26A33 40A05 PDFBibTeX XMLCite \textit{G. Jumarie}, Comput. Math. Appl. 51, No. 9--10, 1367--1376 (2006; Zbl 1137.65001) Full Text: DOI
Guy, Jumarie Lagrange characteristic method for solving a class of nonlinear partial differential equations of fractional order. (English) Zbl 1116.35046 Appl. Math. Lett. 19, No. 9, 873-880 (2006). MSC: 35G20 26A33 PDFBibTeX XMLCite \textit{J. Guy}, Appl. Math. Lett. 19, No. 9, 873--880 (2006; Zbl 1116.35046) Full Text: DOI
Jumarie, Guy Fractionalization of the complex-valued Brownian motion of order \(n\) using Riemann-Liouville derivative. Applications to mathematical finance and stochastic mechanics. (English) Zbl 1099.60025 Chaos Solitons Fractals 28, No. 5, 1285-1305 (2006). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 60G15 91B28 PDFBibTeX XMLCite \textit{G. Jumarie}, Chaos Solitons Fractals 28, No. 5, 1285--1305 (2006; Zbl 1099.60025) Full Text: DOI
Jumarie, Guy A nonrandom variational approach to stochastic linear quadratic Gaussian optimization involving fractional noises (FLQG). (English) Zbl 1106.49048 J. Appl. Math. Comput. 19, No. 1-2, 19-32 (2005). Reviewer: A. Šwierniak (Gliwice) MSC: 49N10 93E20 60H10 60J65 28E99 30B10 91B28 PDFBibTeX XMLCite \textit{G. Jumarie}, J. Appl. Math. Comput. 19, No. 1--2, 19--32 (2005; Zbl 1106.49048) Full Text: DOI