A numerical approach for solving Caputo-Prabhakar distributed-order time-fractional partial differential equation

被引：0

作者：

Khasteh, Mohsen ^{[1
]}

Sheikhani, Amir Hosein Refahi ^{[1
]}

Shariffar, Farhad ^{[2
]}

机构：

[1] Islamic Azad Univ, Fac Math Sci, Dept Appl Math, Lahijan Branch, Lahijan, Iran

[2] Islamic Azad Univ, Dept Appl Math, Fouman & Shaft Branch, Fouman, Iran

来源：

COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS | 2024年 / 12卷 / 03期

关键词：

Distributed order; Caputo-Prabhakar fractional derivative; Shifted Jacobi polynomials; Trapezoid; Numerical method; DIFFUSION-WAVE EQUATION; STABILITY ANALYSIS; MODEL; SCHEME;

D O I：

10.22034/CMDE.2024.57844.2426

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we proposed a numerical method based on the shifted fractional order Jacobi and trapezoid methods to solve a type of distributed partial differential equations. The fractional derivatives are considered in the CaputoPrabhakar type. By shifted fractional-order Jacobi polynomials our proposed method can provide highly accurate approximate solutions by reducing the problem under study to a set of algebraic equations which is technically simpler to handle. In order to demonstrate the error estimates, several lemmas are provided. Finally, numerical results are provided to demonstrate the validity of the theoretical analysis.

引用

页码：571 / 584

页数：14

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