University of Guilan Computational Sciences and Engineering 2783-2503 4 1 2024 04 01 A numerical method for solving a variable-order fractional integral-differential equation 67 78 8488 10.22124/cse.2025.29847.1094 EN Ahmad Sharif Gonbad Kavous University Journal Article 2024 02 15 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. Fractional integral-differential equation Finite difference method Numerical solution derivative order Caputo-Prabhakkar Stability https://cse.guilan.ac.ir/article_8488_415560e0c550a5d231f58b9b7e173772.pdf