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Fractional-order Genocchi-Petrov-Galerkin method for solving time-space fractional Fokker-Planck equations arising from the physical phenomenon. (English) Zbl 1461.65244
Summary: In the current study, we present the fractional-order Genocchi-Petrov-Galerkin method to investigate the approximate solution of time-space fractional Fokker-Planck equations (FFPEs). In the proposed approach, due to fractional Genocchi functions (FGFs) and their operational matrices transform these equations into a system of algebraic equations. The operational matrices of fractional-order integration and derivative are obtained by utilizing Riemann-Liouville fractional integral operator and Caputo fractional derivative, respectively. The convergence analysis of the proposed technique is rigorously discussed. To illustrate the applicability of the error formulas, we present the process of obtaining results for some examples. These examples are carried out to confirm the effectiveness of the proposed method.
MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
35Q84 Fokker-Planck equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
Software:
FODE
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