Finite difference scheme for a fractional telegraph equation with generalized fractional derivative terms

被引：11
|
作者：
Kumar, Kamlesh [1 ]
Pandey, Rajesh K. [1 ,2 ]
Yadav, Swati [1 ]
机构：
[1] Indian Inst Technol BHU Varanasi, Dept Math Sci, Varanasi, UP, India
[2] Indian Inst Technol BHU Varanasi, Ctr Adv Biomat & Tissue Engn, Varanasi 221005, UP, India
来源：
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2019年 / 535卷
关键词：
Generalized fractional derivative; Finite difference scheme; Fractional telegraph equation; PARTIAL INTEGRODIFFERENTIAL EQUATIONS; ADVECTION-DISPERSION EQUATIONS; NUMERICAL-SOLUTIONS; BOUNDED DOMAINS; HILBERT-SPACE; DIFFUSION; APPROXIMATIONS; FORMULATION; SUBJECT; MODELS;
D O I：
10.1016/j.physa.2019.122271
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, a finite difference scheme is presented for the Generalized Time-Fractional Telegraph Equation (GTFTE) defined using Generalized Fractional Derivative (GFD) terms introduced recently. The generalization of fractional derivatives is done by introducing scale and weight functions, and for their particular choices, GFD reduces to Caputo and Riemann-Liouville derivatives. We present the solution behaviour of the GTFTE by changing the weight and scale functions in GFD. The convergence and the stability of the finite difference scheme (FDS) are also presented, and for the numerical simulation of the FDS, we consider examples which validate our numerical method. (C) 2019 Elsevier B.V. All rights reserved.
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页数：15
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