Application of the modified operational matrices in multiterm variable‐order time‐fractional partial differential equations

Abstract

In this paper, we present a novel discrete scheme based on Genocchi polynomials and fractional Laguerre functions to solve multiterm variable-order time-fractional partial differential equations (M-V-TFPDEs) in the large interval. In this purpose, the accurate modified operational matrices are constructed to reduce the problems into a system of algebraic equations. Also, the computational algorithm based on the method and modified operational matrices in the large interval is easily implemented. Furthermore, we discuss the error estimation of the proposed method. Ultimately, to confirm our theoretical analysis and accuracy of numerical approach, several examples are presented. KEYWORDSerror estimation, Genocchi-fractional Laguerre functions, modified operational matrices, variable-order time-fractional partial differential equations MSC CLASSIFICATION

Modified wavelet method for solving multitype variable-order fractional partial differential equations generated from the modeling of phenomena

“…Burgers equation has many applications in modeling of problems as boundary layer behavior, modeling of turbulent fluid, turbulence, sound and shock wave theory and many other works that can be seen in [16,32,33] and references therein. In the aforesaid equations, f 0 , f 1 , 0 and 1 are given functions and the Caputo variable-order time-fractional derivative operator is demonstrated by D (x,t) t u, that is defined as follows [11]:…”

“…In [10], Hajipour et al proposed an accurate discretization technique to solve VO fractional reaction-diffusion problems. In [11], Dehestani et al applied a novel discrete scheme based on Genocchi polynomials and fractional Laguerre functions to solve multiterm VO time-fractional partial differential equations in the large interval. In [12], Lin et al investigated the stability and convergence of an explicit finite-difference approximation for the VO nonlinear fractional diffusion equation.…”

A novel direct method based on the Lucas multiwavelet functions for variable‐order fractional reaction‐diffusion and subdiffusion equations

“…Then, many numerical and analytical schemes have emerged to solve VO fractional problems, including the spline finite difference scheme, 8 the nonstandard finite difference method, 9 discrete schemes based on Genocchi‐fractional Laguerre functions, 10 the pseudo‐operational matrix (POM) method, 11 and the shifted the Legendre–Gauss–Lobatto collocation method 12 …”

Numerical Solution of Variable-Order Time Fractional Weakly Singular Partial Integro-Differential Equations With Error Estimation

“…Several papers have been devoted to the study of variable-order fractional problems, such as variable-order fractional differential equations [17,22,24], variable-order fractional partial integro-differential equations [2,8,20,21,23] and so on. Limited work has been done in the study on VO-TF-PIDEs with the weakly singular kernel.…”