Truncated exponential method for Caputo–Fabrizio optimal control problems

Abstract

ABSTRACT This paper presents a novel and efficient numerical scheme for solving multidimensional optimal control problems governed by the Caputo–Fabrizio fractional derivative (MD‐CFOCP). Unlike traditional approaches based on singular kernel derivatives, our method exploits the nonsingular and exponential nature of the Caputo–Fabrizio operator, enabling a more stable and realistic modeling of systems with short‐term memory and smooth dynamics. The core of the proposed technique lies in approximating both the state and control functions using truncated exponential polynomials (TEPs), combined with an operational matrix of fractional integration tailored to the Caputo–Fabrizio framework. This transforms the original fractional control problem into a system of algebraic equations, which is easier to analyze and solve numerically. A rigorous theoretical analysis is carried out, including error bounds and exponential convergence results. Several numerical examples are provided to demonstrate the high accuracy, computational efficiency, and practical relevance of the proposed method, including comparisons with existing schemes. This study provides a valuable computational framework for researchers and practitioners dealing with fractional dynamic systems with nonsingular memory kernels.