A new operational matrix of fractional derivative based on the generalized Gegenbauer–Humbert polynomials to solve fractional differential equations

Abstract

In this paper, a new type of wavelet method to solve fractional differential equations (linear or nonlinear) is proposed. The proposed method is based on the generalized Gegenbauer–Humbert polynomial. First, we derived the operational matrices for integer and fractional order derivatives. Then, using these operational matrices with the proposed method, we transformed the given problem into a system of algebraic equations. Then, some linear and nonlinear examples were considered and discussed to confirm the efficiency and accuracy of the proposed method.