Solution of Some Types for Composition Fractional Order Differential Equations Corresponding to Optimal Control Problems

Abstract

The approximate solution for solving a class of composition fractional order optimal control problems (FOCPs) is suggested and studied in detail. However, the properties of Caputo and Riemann-Liouville derivatives are also given with complete details on Chebyshev approximation function to approximate the solution of fractional differential equation with different approach. Also, the relation between Caputo and Riemann-Liouville of fractional derivative took a big role for simplifying the fractional differential equation that represents the constraints of optimal control problems. The approximate solutions are defined on interval [0,1] and are compared with the exact solution of order one which is an important condition to support the working method. Finally, illustrative examples are included to confirm the efficiency and accuracy of the proposed method.

The Necessary and Sufficient Optimality Conditions for a System of FOCPs with Caputo–Katugampola Derivatives

“…Approximate results and the necessary optimality conditions for a class composition FODEs corresponding to OCPs suggested and studied by Qasim Hasan S, et al 10 .…”

Stabilization of Multi Fractional order Differential Equation with Delay time and Feedback Control

“…Then, Li and et al are studying of the global stability problem for feedback control systems of impulsive fractional differential equations on networks [5]. Another direction studied by Qasim and et for some classes with composition FOCPs as in [6]. The stabilization and destabilization of fractional oscillators via a delayed feedback control has been considered by Čermák et al in [7].…”