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A fractional characteristic method for solving fractional partial differential equations. (English) Zbl 1216.35166
Summary: The method of characteristics has played a very important role in mathematical physics. Previously, it has been employed to solve the initial value problem for partial differential equations of first order. In this work, we propose a new fractional characteristic method and use it to solve some fractional partial differential equations.
MSC:
35R11Fractional partial differential equations
26A33Fractional derivatives and integrals (real functions)
35A24Methods of ordinary differential equations for PDE
References:
[1]Courant, R.; Hilbert, D.: Methods of mathematical physics, Partial differential equations 2 (1962) · Zbl 0099.29504
[2]Jeffreys, H.; Jeffreys, B.: Methods of mathematical physics, (2000)
[3]Delgado, M.: The Lagrange–charpit method, SIAM rev. 39, 298-304 (1997) · Zbl 0884.35025 · doi:10.1137/S0036144595293534
[4]Jumarie, G.: Modified Riemann–Liouville derivative and fractional Taylor series of non-differentiable functions further results, Comput. math. Appl. 51, 1367-1376 (2006) · Zbl 1137.65001 · doi:10.1016/j.camwa.2006.02.001
[5]Jumarie, G.: Lagrange characteristic method for solving a class of nonlinear partial differential equations of fractional order, Appl. math. Lett. 19, 873-880 (2006) · Zbl 1116.35046 · doi:10.1016/j.aml.2005.10.016
[6]Kolwankar, K. M.; Gangal, A. D.: Fractional differentiability of nowhere differentiable functions and dimensions, Chaos 6, 505-513 (1996) · Zbl 1055.26504 · doi:10.1063/1.166197
[7]Kolwankar, K. M.; Gangal, A. D.: Hölder exponents of irregular signals and local fractional derivatives, Pramana J. Phys. 48, 49-68 (1997)
[8]Kolwankar, K. M.; Gangal, A. D.: Local fractional Fokker–Planck equation, Phys. rev. Lett. 80, 214-217 (1998) · Zbl 0945.82005 · doi:10.1103/PhysRevLett.80.214
[9]Sun, H. G.; Chen, W.: Fractal derivative multi-scale model of fluid particle transverse accelerations in fully developed turbulence, Sci. China ser. E 52, 680-683 (2009)
[10]Chen, W.; Sun, H. G.: Multiscale statistical model of fully-developed turbulence particle accelerations, Modern phys. Lett. B 23, 449-452 (2009)
[11]Cresson, J.: Scale calculus and the Schrödinger equation, J. math. Phys. 44, No. 11, 4907-4938 (2003) · Zbl 1062.39022 · doi:10.1063/1.1618923
[12]Parvate, A.; Gangal, A. D.: Calculus on fractal subsets of real line–I: formulation, Fractals 17, 53-81 (2009) · Zbl 1173.28005 · doi:10.1142/S0218348X09004181
[13]Jumarie, G.: New stochastic fractional models for malthusian growth, the Poissonian birth process and optimal management of populations, Math. comput. Modelling 44, 231-254 (2006) · Zbl 1130.92043 · doi:10.1016/j.mcm.2005.10.003
[14]Jumarie, G.: Laplace’s transform of fractional order via the Mittag-Leffler function and modified Riemann–Liouville derivative, Appl. math. Lett. 22, 1659-1664 (2009) · Zbl 1181.44001 · doi:10.1016/j.aml.2009.05.011
[15]Almeida, R.; Malinowska, A. B.; Torres, D. F. M.: A fractional calculus of variations for multiple integrals with application to vibrating string, J. math. Phys. 51, 033503 (2010)
[16]Wu, G. C.; Lee, E. W. M.: Fractional variational iteration method and its application, Phys. lett. A 374, 2506-2509 (2010)
[17]Malinowska, A. B.; Ammi, M. R. Sidi; Torres, D. F. M.: Composition functionals in fractional calculus of variations, Commun. frac. Calc. 1, 32-40 (2010)
[18]Wu, G. C.: A fractional Lie group method for anonymous diffusion equations, Commun. frac. Calc. 1, 23-27 (2010)