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Oliveira DS, Sousa JVDC, Frederico GSF. Pseudo-fractional operators of variable order and applications. Soft comput 2022. [DOI: 10.1007/s00500-022-06945-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels. MATHEMATICS 2021. [DOI: 10.3390/math9192355] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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.
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Ibrahim AG, Elmandouh AA. Euler–Lagrange equations for variational problems involving the Riesz–Hilfer fractional derivative. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2020. [DOI: 10.1080/16583655.2020.1764245] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- A. G. Ibrahim
- Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa, Saudi Arabia
| | - A. A. Elmandouh
- Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa, Saudi Arabia
- Department of Mathematics, College of Science, Mansoura University, Mansoura, Egypt
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Conserved Quantity and Adiabatic Invariant for Hamiltonian System with Variable Order. Symmetry (Basel) 2019. [DOI: 10.3390/sym11101270] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Hamiltonian mechanics plays an important role in the development of nonlinear science. This paper aims for a fractional Hamiltonian system of variable order. Several issues are discussed, including differential equation of motion, Noether symmetry, and perturbation to Noether symmetry. As a result, fractional Hamiltonian mechanics of variable order are established, and conserved quantity and adiabatic invariant are presented. Two applications, fractional isotropic harmonic oscillator model of variable order and fractional Lotka biochemical oscillator model of variable order are given to illustrate the Methods and Results.
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Rosa S, Torres DF. Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection. CHAOS SOLITONS & FRACTALS 2018. [DOI: 10.1016/j.chaos.2018.10.021] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
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