Browsing by Author "Lakestani, Mehrdad"

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Cubic B-Spline Approach for Solving Fractional Optimal Control Problems in the Caputo-Fabrizio Sense
(Univ Nis, Fac Sci Math, 2025) Lakestani, Mehrdad; Tuntas, Remzi
In this paper, a numerical method is presented for solving fractional optimal control problems (FOCPs) in the Caputo-Fabrizio sense using cubic B-spline functions. Operational matrices for ordinary and fractional derivatives are constructed to facilitate the transformation of the FOCP into a nonlinear programming problem. The Lagrange multiplier method is applied to obtain the optimal solution. Additionally, the error bounds for the proposed approximations are derived to ensure the reliability of the method. The efficiency and accuracy of the approach are demonstrated through three numerical examples, confirming its effectiveness in solving fractional control problems.
Efficient Solution for Multi-Delay Fractional Optimal Control Problems Via Cubic B-Splines
(Wiley, 2025) Lakestani, Mehrdad; Tuntas, Remzi
In this article, we address multi-delay fractional optimal control problems using cubic B-spline functions. First, the properties of cubic B-spline functions are presented, and their operational matrices for derivatives of both ordinary and fractional orders are derived. These matrices are then utilized to transform the original problem into an optimization problem, which is subsequently converted into a system of algebraic equations using Lagrange multipliers. The approximate solution is obtained by solving this algebraic system. Numerical results are provided to demonstrate the validity, effectiveness, and stability of the proposed method.