Solution Method for Systems of Nonlinear Fractional Differential Equations Using Third Kind Chebyshev Wavelets

Abstract

Chebyshev Wavelets of the third kind are proposed in this study to solve nonlinear systems of FDEs. The main goal of the method is to convert the nonlinear FDE into a nonlinear system of algebraic equations that can be easily solved using matrix methods. In order to achieve this, we first generate the operational matrices for the fractional integration using third kind Chebyshev Wavelets and block-pulse functions (BPF) for function approximation. Since the obtained operational matrices are sparse, the obtained numerical method is fast and computationally efficient. The original nonlinear FDE is transformed into a system of algebraic equations in a vector-matrix form using the obtained operational matrices. The collocation points are then used to solve the system of algebraic equations. Numerical results for various examples and comparisons are presented.