On the Optimal Control Existence for Multi-Term Multi-Order Fractional Differential Equations with Impulsive Conditions

HuiChol Choe (), SuRim Han (), SunAe Pak (), GwangHyok Kim (), GyongGuk Kim () and DanOh U ()
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HuiChol Choe: Kim Il Sung University
SuRim Han: Kim Il Sung University
SunAe Pak: Kim Il Sung University
GwangHyok Kim: Kim Il Sung University
GyongGuk Kim: Kim Il Sung University
DanOh U: Kim Il Sung University

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 4, 24 pages

Abstract: Abstract In this paper, we study the existence of solutions to nonlinear impulsive fractional optimal control problems, where the state equations are linear with respect to their control variables and governed by multi-order systems of multi-term fractional differential ones. Initial and impulsive conditions are also given. The performance index is considered as an integral functional, whose integrand is continuous with respect to its variables. At first, we transform the state equations into the integral ones to prove the existence and uniqueness of solutions, assuming that the nonlinear functions in the equations are Lipschitz continuous in a bounded domain. Secondly, using the generalized Arzela-Ascoli theorem, we establish that sets of our admissible processes are compact ones in a piecewise continuous function space to show the optimal control existence.

Keywords: Optimal control; Impulsive condition; Fractional differential equation; Multi-order system; Initial value problem; 34A08; 49J15; 49J45; 49N25 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02830-1

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