Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels

Faïçal Ndaïrou and Delfim F. M. Torres
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Faïçal Ndaïrou: Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Delfim F. M. Torres: Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Mathematics, 2021, vol. 9, issue 19, 1-17

Abstract: Fractional optimal control problems via a wide class of fractional operators with a general analytic kernel are introduced. Necessary optimality conditions of Pontryagin type for the considered problem are obtained after proving a Gronwall type inequality as well as results on continuity and differentiability of perturbed trajectories. Moreover, a Mangasarian type sufficient global optimality condition for the general analytic kernel fractional optimal control problem is proved. An illustrative example is discussed.

Keywords: fractional operators with general analytic kernels; Gronwall’s inequality; optimal control and Pontryagin’s extremals; Mangasarian sufficient optimality condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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