Fractional truncated exponential method for linear fractional optimal control problems

Said Ounamane, Lakhlifa Sadek, Bouchra Abouzaid and El Mostafa Sadek

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 232, issue C, 408-426

Abstract: 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.

Keywords: Riemann–Liouville fractional integral (RLFI); Galerkin method; CFD; FOCP; Truncated exponential functions; Inequality constraints; Error estimation and convergence analysis (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:232:y:2025:i:c:p:408-426

DOI: 10.1016/j.matcom.2025.01.009

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