Optimal Control for a Variable-Order Diffusion-Wave Equation With a Reaction Term; a Numerical Study
| dc.contributor.author | Megahed, F. | |
| dc.contributor.author | Shatta, S.A. | |
| dc.contributor.author | Baleanu, D. | |
| dc.contributor.author | Sweilam, N.H. | |
| dc.date.accessioned | 2024-09-18T10:59:49Z | |
| dc.date.accessioned | 2025-09-18T12:09:22Z | |
| dc.date.available | 2024-09-18T10:59:49Z | |
| dc.date.available | 2025-09-18T12:09:22Z | |
| dc.date.issued | 2024 | |
| dc.description.abstract | In this paper, optimal control for a variable-order diffusion-wave equation with a reaction term is numerically studied, where the variable-order operator is defined in the sense of Caputo proportional constant. Necessary optimality conditions for the control problem are derived. Existence and uniqueness for the solutions of fractional optimal control problem are derived. The nonstandard weighted average finite difference method and the nonstandard leap-frog method are developed to study numerically the proposed problem. Moreover, the stability analysis of the methods is proved. Finally, in order to characterise the memory property of the proposed model, three test examples are given. It is found that the nonstandard weighted average finite difference method can be applied to study such variable-order fractional optimal control problems simply and effectively. © 2024 The Author(s) | en_US |
| dc.identifier.citation | Sweilam, N.H...et al (2024). "Optimal control for a variable-order diffusion-wave equation with a reaction term; A numerical study", Partial Differential Equations in Applied Mathematics, Vol. 10. | en_US |
| dc.identifier.doi | 10.1016/j.padiff.2024.100658 | |
| dc.identifier.issn | 2666-8181 | |
| dc.identifier.scopus | 2-s2.0-85189877766 | |
| dc.identifier.uri | https://doi.org/10.1016/j.padiff.2024.100658 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12416/11383 | |
| dc.language.iso | en | en_US |
| dc.publisher | Elsevier B.V. | en_US |
| dc.relation.ispartof | Partial Differential Equations in Applied Mathematics | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Constant-Proportional-Caputo Hybrid Fractional Operator | en_US |
| dc.subject | Diffusion-Wave Equation With A Reaction Term | en_US |
| dc.subject | Lagrange Method For The Optimal Control Of Partial Differential Equations | en_US |
| dc.subject | Nonstandard Leap-Frog Method | en_US |
| dc.subject | Nonstandard Weighted Average Finite Difference Method | en_US |
| dc.subject | Optimality System | en_US |
| dc.subject | Variable-Order Fractional Derivatives | en_US |
| dc.title | Optimal Control for a Variable-Order Diffusion-Wave Equation With a Reaction Term; a Numerical Study | en_US |
| dc.title | Optimal control for a variable-order diffusion-wave equation with a reaction term; A numerical study | tr_TR |
| dc.type | Article | en_US |
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| gdc.description.department | Çankaya University | en_US |
| gdc.description.departmenttemp | Sweilam N.H., Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt; Megahed F., Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt; Shatta S.A., Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt; Baleanu D., Department of Mathematics, Cankaya University, Turkey, Institute of Space Sciences, Bucharest, Magurele, Romania | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
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| gdc.description.volume | 10 | en_US |
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| gdc.oaire.keywords | Optimality system | |
| gdc.oaire.keywords | Applied mathematics. Quantitative methods | |
| gdc.oaire.keywords | Variable-order fractional derivatives | |
| gdc.oaire.keywords | Constant-proportional-Caputo hybrid fractional operator | |
| gdc.oaire.keywords | Nonstandard leap-frog method | |
| gdc.oaire.keywords | Lagrange method for the optimal control of partial differential equations | |
| gdc.oaire.keywords | Diffusion-wave equation with a reaction term | |
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| gdc.virtual.author | Baleanu, Dumitru | |
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