Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels
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 differe...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/19/2355 |
| _version_ | 1827680747976130560 |
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| author | Faïçal Ndaïrou Delfim F. M. Torres |
| author_facet | Faïçal Ndaïrou Delfim F. M. Torres |
| author_sort | Faïçal Ndaïrou |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T06:55:57Z |
| format | Article |
| id | doaj.art-5ab48b997b8446c697d672d207247879 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T06:55:57Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5ab48b997b8446c697d672d2072478792023-11-22T16:29:07ZengMDPI AGMathematics2227-73902021-09-01919235510.3390/math9192355Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels Faïçal Ndaïrou0Delfim F. M. Torres1Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, PortugalCenter for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, PortugalFractional 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.https://www.mdpi.com/2227-7390/9/19/2355fractional operators with general analytic kernelsGronwall’s inequalityoptimal control and Pontryagin’s extremalsMangasarian sufficient optimality condition |
| spellingShingle | Faïçal Ndaïrou Delfim F. M. Torres Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels Mathematics fractional operators with general analytic kernels Gronwall’s inequality optimal control and Pontryagin’s extremals Mangasarian sufficient optimality condition |
| title | Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels |
| title_full | Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels |
| title_fullStr | Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels |
| title_full_unstemmed | Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels |
| title_short | Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels |
| title_sort | optimal control problems involving combined fractional operators with general analytic kernels |
| topic | fractional operators with general analytic kernels Gronwall’s inequality optimal control and Pontryagin’s extremals Mangasarian sufficient optimality condition |
| url | https://www.mdpi.com/2227-7390/9/19/2355 |
| work_keys_str_mv | AT faicalndairou optimalcontrolproblemsinvolvingcombinedfractionaloperatorswithgeneralanalytickernels AT delfimfmtorres optimalcontrolproblemsinvolvingcombinedfractionaloperatorswithgeneralanalytickernels |