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

Document Type : Research Paper


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


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.‎