An Analytic Study on the Approximate Solution of a Nonlinear Time-Fractional Cauchy Reaction-Diffusion Equation With the Mittag-Leffler Law
| dc.contributor.author | Ilie, Mousa | |
| dc.contributor.author | Mirzazadeh, Mohammad | |
| dc.contributor.author | Baleanu, Dumitru | |
| dc.contributor.author | Hosseini, Kamyar | |
| dc.date.accessioned | 2022-03-11T13:52:42Z | |
| dc.date.accessioned | 2025-09-18T12:49:30Z | |
| dc.date.available | 2022-03-11T13:52:42Z | |
| dc.date.available | 2025-09-18T12:49:30Z | |
| dc.date.issued | 2021 | |
| dc.description | Ilie, Mousa/0000-0002-1165-8815; Hosseini, Kamyar/0000-0001-7137-1456 | en_US |
| dc.description.abstract | The main aim of the current article is considering a nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law and deriving its approximate analytical solution in a systematic way. More precisely, after reformulating the nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law, its approximate analytical solution is derived formally through the use of the homotopy analysis transform method (HATM) which is based on the homotopy method and the Laplace transform. The existence and uniqueness of the solution of the nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law are also studied by adopting the fixed-point theorem. In the end, by considering some two- and three-dimensional graphs, the influence of the order of time-fractional operator on the displacement is examined in detail. | en_US |
| dc.identifier.citation | Hosseini, Kamyar...et al. (2021). "An analytic study on the approximate solution of a nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law", Mathematical Methods in the Applied Sciences, Vol. 44, no. 8, pp. 6247-6258. | en_US |
| dc.identifier.doi | 10.1002/mma.7059 | |
| dc.identifier.issn | 0170-4214 | |
| dc.identifier.issn | 1099-1476 | |
| dc.identifier.scopus | 2-s2.0-85102282825 | |
| dc.identifier.uri | https://doi.org/10.1002/mma.7059 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12416/12368 | |
| dc.language.iso | en | en_US |
| dc.publisher | Wiley | en_US |
| dc.relation.ispartof | Mathematical Methods in the Applied Sciences | |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Approximate Analytical Solution | en_US |
| dc.subject | Existence And Uniqueness Of The Solution | en_US |
| dc.subject | Fixed‐ | en_US |
| dc.subject | Point Theorem | en_US |
| dc.subject | Homotopy Analysis Transform Method | en_US |
| dc.subject | Mittag– | en_US |
| dc.subject | Leffler Law | en_US |
| dc.subject | Nonlinear Time‐ | en_US |
| dc.subject | Fractional Cauchy Reaction– | en_US |
| dc.subject | Diffusion Equation | en_US |
| dc.title | An Analytic Study on the Approximate Solution of a Nonlinear Time-Fractional Cauchy Reaction-Diffusion Equation With the Mittag-Leffler Law | en_US |
| dc.title | An analytic study on the approximate solution of a nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law | tr_TR |
| dc.type | Article | en_US |
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| gdc.author.id | Ilie, Mousa/0000-0002-1165-8815 | |
| gdc.author.id | Hosseini, Kamyar/0000-0001-7137-1456 | |
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| gdc.author.wosid | Ilie, Mousa/Aao-4295-2021 | |
| gdc.author.wosid | Hosseini, Kamyar/J-7345-2019 | |
| gdc.author.wosid | Baleanu, Dumitru/B-9936-2012 | |
| gdc.author.wosid | Mirzazadeh, Mohammad/Y-3202-2019 | |
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| gdc.description.department | Çankaya University | en_US |
| gdc.description.departmenttemp | [Hosseini, Kamyar; Ilie, Mousa] Islamic Azad Univ, Rasht Branch, Dept Math, Rasht, Iran; [Mirzazadeh, Mohammad] Univ Guilan, Dept Engn Sci, Fac Engn & Technol, Rudsar, Iran; [Baleanu, Dumitru] Cankaya Univ, Fac Arts & Sci, Dept Math, TR-06530 Ankara, Turkey; [Baleanu, Dumitru] Inst Space Sci, Magurele, Romania; [Baleanu, Dumitru] China Med Univ, Dept Med Res, Taichung, Taiwan | en_US |
| gdc.description.endpage | 6258 | en_US |
| gdc.description.issue | 8 | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
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| gdc.description.startpage | 6247 | en_US |
| gdc.description.volume | 44 | en_US |
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| gdc.oaire.keywords | Reaction-diffusion equations | |
| gdc.oaire.keywords | Mittag-Leffler law | |
| gdc.oaire.keywords | approximate analytical solution | |
| gdc.oaire.keywords | Transform methods (e.g., integral transforms) applied to PDEs | |
| gdc.oaire.keywords | Initial-boundary value problems for second-order parabolic equations | |
| gdc.oaire.keywords | fixed-point theorem | |
| gdc.oaire.keywords | homotopy analysis transform method | |
| gdc.oaire.keywords | Fractional partial differential equations | |
| gdc.oaire.keywords | existence and uniqueness of the solution | |
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