Numerical scheme to solve a class of variable—order Hilfer—Prabhakar fractional differential equations with Jacobi wavelets polynomials

Abstract

In this paper, we introduced a numerical approach for solving the fractional differential equations with a type of variable-order Hilfer-Prabhakar derivative of order μ(t) and ν(t). The proposed method is based on the Jacobi wavelet collocation method. According to this method, an operational matrix is constructed. We use this operational matrix of the fractional derivative of variable-order to reduce the solution of the linear fractional equations to the system of algebraic equations. Theoretical considerations are discussed. Finally, some numerical examples are presented to demonstrate the accuracy of the proposed method.