Numerical solution of nonlinear mixed Fredholm-Volterra integro-differential equations of fractional order by Bernoulli wavelets

Keshavarz, Elham; Ordokhani, Yadollah; Razzaghi, Mohsen

Numerical solution of nonlinear mixed Fredholm-Volterra integro-differential equations of fractional order by Bernoulli wavelets

Document Type : Research Paper

Authors

¹ Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

² Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762

Abstract

In this paper, a numerical method for solving a class of nonlinear mixed Fredholm-Volterra integro-diﬀerential equations of fractional order is presented. The method is based upon Bernoulli wavelets approximations. The operational matrix of fractional order integration for Bernoulli wavelets is utilized to reduce the solution of the nonlinear fractional integro-diﬀerential equations to system of algebraic equations. Illustrative examples are included to demonstrate the eﬃciency and accuracy of the method.

Keywords