Chebyshev Wavelet Operational Matrix of Fractional Derivative Through Wavelet-Polynomial Transformation and Its Applications on Fractional Order Differential Equations

Abstract

In this paper, new numerical method based on Chebyshev wavelet operational matrix of fractional derivative is presented. The known Chebyshev Wavelets is presented first. Then, we derived the operational matrix of fractional order derivative (OMOFOD), through wavelet transformation matrix which was utilized together with spectral and collocation methods to reduce the linear and nonlinear fractional differential equations (FDEs) to a system of algebraic equations respectively. Our results in solving different linear and nonlinear FDEs confirm the applicability and accuracy of the proposed method.