A new approach for solving variable order differential equations based on Bernstein polynomials with Prabhakar function. Issue 5 (12th August 2020) - Derakhshan, Mohammadhossein; Aminataei, Azim
Abstract : In this article, an accurate and robust numerical method is proposed to solve a class of nonlinear variable order fractional differential equations (FDEs) in the Caputo‐Prabhakar sense by using Bernstein polynomials (BPs). Here, we use the BPs to obtain operational matrices. This operational matrices of BPs are utilized to transform the studied variable order FDEs into a system of algebraic equations after dispersing the variable which greatly simplifies the solution process. By solving the system of equations, the numerical solutions are acquired. Some examples are provided in order to demonstrate the accuracy of the proposed method.