Fractional truncated exponential method for linear fractional optimal control problems

作     者：Ounamane, Said Sadek, Lakhlifa Abouzaid, Bouchra Sadek, El Mostafa 

作者机构：Chouaib Doukkali Univ Natl Sch Appl Sci El Jadida LabSIPE El Jadida Morocco 

出 版 物：《MATHEMATICS AND COMPUTERS IN SIMULATION》 (Math Comput Simul)

年 卷 期：2025年第232卷

页      面：408-426页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0835[工学-软件工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Riemann-Liouville fractional integral (RLFI) Galerkin method CFD FOCP Truncated exponential functions Inequality constraints Error estimation and convergence analysis 

摘      要：In this paper, we employ the Caputo fractional derivative (CFD) approach and utilize the truncated exponential method to tackle linear fractional optimal control problems (FOCPs) with equality and inequality constraints in multi-dimensional settings. By applying the truncated exponential method, we transform the FOCP into a system of algebraic equations that can be readily solved. Our analysis extends to the convergence and error estimation (EE) of truncated exponential method polynomials, and we introduce a residual correction procedure to refine error estimates. To assess the effectiveness and applicability of the proposed method, we conduct experiments on three different examples and compare our results with those of the previously obtained ones. Our findings yield very satisfactory results, and in some cases, we obtain exact solutions.