a numerical method for solving a variable-order fractional integral-differential equation

In this paper, a numerical method based on finite differences is presented for numerically solving a fractional integral-differential equation of variable order with prabhakar integral and caputo-prabhakkar fractional derivative. using the proposed method, an approximate solution of the desired equation is obtained from solving a system of linear equations. the stability of the method is investigated and it is shown that the proposed method is stable under certain conditions. three examples are presented to demonstrate the efficiency and accuracy of the proposed method.