A New Accurate Horadam Wavelet Method for Solving Fractional Optimal Control Problems

Abstract

Recently, fractional optimal control problems (FOCPs) have attracted significant attention due to their ability to describe dynamical systems. In this study, an efficient computational framework is proposed based on a novel class of wavelet functions, called Horadam wavelets (HWs), to solve FOCPs involving Caputo‐type fractional differential equations. To this aim, a new exact formulation of the Riemann–Liouville fractional integral operator (RLFIO) for HWs is derived, and a Galerkin strategy combined with Gauss–Legendre quadrature is employed to construct accurate approximations of the optimal state and control functions. This proposed method transforms the original FOCPs into a system of algebraic equations with reduced computational complexity. A convergence analysis is provided. Moreover, several numerical examples confirm that the presented scheme provides highly accurate solutions and exhibits superior performance compared with some existing numerical techniques. To demonstrate the efficiency of the proposed method, the final example investigates a real‐world cancer treatment model.