Euler Wavelet Method as a Numerical Approach for the Solution of Nonlinear Systems of Fractional Differential Equations

Abstract

In this paper, a numerical approach for solving systems of nonlinear fractional differential equations (FDEs) is presented Using the Euler wavelets technique and associated operational matrices for fractional integration, we try to solve those systems of FDEs. The method's major objective is to transform the nonlinear FDE into a nonlinear system of algebraic equations that is straightforward to solve with matrix techniques. The Euler wavelets are constructed using Euler polynomials, which have fewer terms than most other polynomials used to construct other types of wavelets, therefore, using Euler wavelets for the numerical approach provides sparse operational matrices. Thanks to the sparsity of those operational matrices, the proposed numerical approach requires less computation and takes less time to evaluate. The approach described here is also applicable to systems of fractional differential equations with variable orders. To illustrate the strength and performance of the method, four numerical examples are provided.