### Walsh functions and their applications to solving nonlinear fractional Volterra integro-differential equation

Document Type : Research Paper

Authors

1 Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

3 Department of Mathematics, Khalkhal Branch, Islamic Azad University, Khalkhal, Iran

Abstract

In this article‎, ‎we extended an efficient computational‎ ‎method based on Walsh operational matrix to find an approximate‎ ‎solution of nonlinear fractional order Volterra integro-differential‎ ‎equation‎, ‎First‎, ‎we present the fractional Walsh operational‎ ‎matrix of integration and differentiation‎. ‎Then by applying this‎ ‎method‎, ‎the nonlinear fractional Volterra integro-differential‎ ‎equation is reduced into a system of algebraic equation‎. ‎The‎ ‎benefits of this method are the low-cost of setting up the equations‎ ‎without applying any projection method such as collocation‎, ‎Galerkin‎, ‎etc‎. ‎The results show that the method is very accuracy and ‎efficiency.‎

Keywords

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###### Volume 12, Issue 2November 2021Pages 1577-1589
• Receive Date: 17 February 2020
• Revise Date: 16 May 2021
• Accept Date: 28 June 2021