Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets

Abstract

In this work, we propose a numerical method based on the generalized sine-cosine wavelets for solving multi-order fractional differential equations. After introducing generalized sine-cosine wavelets, the operational matrix of Riemann-Liouville fractional integration is constructed using the properties of the block-pulse functions. The fractional derivative in the problem is considered in the Caputo sense. This method reduces the considered problem to the problem of solving a system of nonlinear algebraic equations. Finally, some examples are included to demonstrate the applicability of the new approach.

Keywords

• generalized sine-cosine wavelet
• operational matrix of fractional integration
• multi-order fractional differential equations
• block-pulse functions
• operational matrix of fractional integration