Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 12 2 2021 11 01 Walsh functions and their applications to solving nonlinear fractional Volterra integro-differential equation 1577 1589 5286 10.22075/ijnaa.2021.19846.2108 EN Amirahmad Khajehnasiri Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran Reza Ezzati Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran Akbar Jafari Shaerlar Department of Mathematics, Khalkhal Branch, Islamic Azad University, Khalkhal, Iran Journal Article 2020 02 17 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.‎ https://ijnaa.semnan.ac.ir/article_5286_cb74b28ee3138dd8b107a61f879d2ec9.pdf