Approximate solutions for a certain class of fractional optimal control problems using Laguerre collocation method

Abstract

In this paper, an approximate formula of the fractional derivatives (Caputo sense) is derived. The proposed formula is based on the generalized Laguerre polynomials. Special attention is given to study the convergence analysis of the presented formula. The spectral Laguerre collocation method is presented for solving a class of fractional optimal control problems (FOCPs). The properties of Laguerre polynomials approximation and Rayleigh-Ritz method are used to reduce FOCPs to solve a system of algebraic equations which solved using Newton iteration method. Numerical results are provided to confirm the theoretical results and the efficiency of the proposed method.