The Invariant Subspace Method for Solving Nonlinear Fractional Partial Differential Equations With Generalized Fractional Derivatives
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Date
2020
Journal Title
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Springeropen
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GOLD
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No
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Abstract
In this paper, we show that the invariant subspace method can be successfully utilized to get exact solutions for nonlinear fractional partial differential equations with generalized fractional derivatives. Using the invariant subspace method, some exact solutions have been obtained for the time fractional Hunter-Saxton equation, a time fractional nonlinear diffusion equation, a time fractional thin-film equation, the fractional Whitman-Broer-Kaup-type equation, and a system of time fractional diffusion equations.
Description
Abdel Kader, Abass/0000-0002-9658-1430; Abdel Latif, Mohamed/0000-0002-9013-1017
Keywords
Fractional Differential Equations, Generalized Fractional Derivative, Invariant Subspace Method, Fractional differential equations, Mathematical analysis, Quantum mechanics, Invariant subspace, Convergence Analysis of Iterative Methods for Nonlinear Equations, Generalized fractional derivative, Differential equation, QA1-939, FOS: Mathematics, Anomalous Diffusion Modeling and Analysis, Invariant subspace method, Numerical Analysis, Time-Fractional Diffusion Equation, Linear subspace, Physics, Fractional calculus, Pure mathematics, Statistical and Nonlinear Physics, Partial differential equation, Derivative-Free Methods, Invariant (physics), Fractional Derivatives, Physics and Astronomy, Modeling and Simulation, Mathematical physics, Physical Sciences, Nonlinear system, Mathematics, Rogue Waves in Nonlinear Systems, Thin films, Fractional derivatives and integrals, invariant subspace method, fractional differential equations, Fractional partial differential equations, generalized fractional derivative
Fields of Science
01 natural sciences, 0103 physical sciences
Citation
Latif, Mohamed S. Abdel; Kader, Abass H. Abdel; Baleanu, Dumitru (2020). "The invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivatives", Advances in Difference Equations, Vol. 2020, No. 1.
WoS Q
Q1
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OpenCitations Citation Count
8
Source
Advances in Difference Equations
Volume
2020
Issue
1
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CrossRef : 7
Scopus : 16
SCOPUS™ Citations
16
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Web of Science™ Citations
14
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