Combination of Ritz-Galerkin Method and Fractional-order Generalized Lucas Functions for Distributed-order Fractional Optimal Control Problems

چکیده مقاله

This manuscript presents a new computational method for solving a class of distributed-order fractional optimal control problems. The proposed method is based on the Ritz-Galerkin method. To this end, we define fractional order generalized Lucas functions. These functions have three free parameters that can affect the accuracy of the methods designed with them. To implement the desired scheme, we present an extra Caputo pseudo-operational matrix, and using it, we propose an extra distributed-order fractional pseudo-operational matrix. With the help of the Ritz-Galerkin method and the mentioned preliminaries, the considered problem is converted to a system of algebraic equations, which can be solved by Newton’s iterative method. We substantiate the superiority of our approach by rigorously comparing it with existing techniques in the literature, affirming its high efficiency. © The Author(s), under exclusive licence to Shiraz University 2026.