Numerical solution of nonlinear multi-term fractional differential equations based on spline Riesz wavelets

Abstract

In this article, a direct method for the numerical solution of multi-term fractional differential equations is proposed. The method is based on transforming the original equation into an equivalent system of multi-order fractional equations. This system is discretized by fractional derivatives of Riesz spline wavelets and the collocation method. Then the original problem is transformed into a system of algebraic equations and can be easily solved. Finally, several numerical examples and comparisons with other methods are provided to demonstrate the efficiency and accuracy of our approach.