Numerical solution of the mixed Volterra-Fredholm integro-differential multi-term equations of fractional order

被引：11

作者：

Roohollahi, A. ^{[1
]}

Ghazanfari, B. ^{[1
]}

Akhavan, S. ^{[2
]}

机构：

[1] Lorestan Univ, Dept Math, Khorramabad, Iran

[2] Islamic Azad Univ, Dept Math, Khomeinishahr Branch, Khomeinishahr Isfahan, Iran

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2020年 / 376卷 / 376期

关键词：

Mixed Volterra-Fredholm; Fractional integro-differential equations; Generalized block pulse function; Ordinary differential equation; Fractional calculus; Multi-order fractional; DIFFERENTIAL-EQUATIONS;

D O I：

10.1016/j.cam.2020.112828

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper aims to introduce two effective numerical approaches for solving the mixed Volterra-Fredholm integro-differential equation of fractional order and multi-order with initial values. Despite the fact that the second approach transfers the integro-differential equations into a system of algebraic equations through the usage of operational matrices, these problems can be transferred to a system of algebraic equations by expanding the solution's highest order derivative through the block pulse functions (BPFs). This is done by using the generalized operational matrices of BPFs for differentiation along with the fractional calculus properties in the first scheme, in which convergence of the solution obtained has been shown in the following. The accuracy and applicability of two proposed approaches will be compared by some relevant numerical examples, for which the exact solution is known. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：19

共 30 条

[21] Numerical comparison of methods for solving linear differential equations of fractional order [J].