Solving the Fractional Optimal Control of a Spring-Mass-Viscodamper System with Caputo–Fabrizio Fractional Operator

The present paper investigates and develops a new technique based on the Chebyshev cardinal functions for solving fractional optimal control problems of a spring-mass-viscodamper system involving the Caputo–Fabrizio fractional operator. Through the way, the new operational matrix of Caputo–Fabrizio fractional operator is achieved for Chebyshev cardinal functions. Moreover, we apply a direct approach for solving the fractional optimal control problem by reducing the original problem to a system of algebraic equations. We also compare this new fractional operator with well known Caputo fractional derivative in the numerical example that shows Caputo–Fabrizio fractional operator may provide better results in terms of settling time of the system.