Solving Differential Equations of Fractional Order Using an Optimization Technique Based on Training Artificial Neural Network
| dc.contributor.author | Ahmadian, A. | |
| dc.contributor.author | Effati, S. | |
| dc.contributor.author | Salahshour, S. | |
| dc.contributor.author | Baleanu, D. | |
| dc.contributor.author | Pakdaman, M. | |
| dc.date.accessioned | 2020-03-19T11:56:25Z | |
| dc.date.accessioned | 2025-09-18T15:44:26Z | |
| dc.date.available | 2020-03-19T11:56:25Z | |
| dc.date.available | 2025-09-18T15:44:26Z | |
| dc.date.issued | 2017 | |
| dc.description | Salahshour, Soheil/0000-0003-1390-3551; Ahmadian, Ali/0000-0002-0106-7050; Effati, Sohrab/0000-0001-9752-0034; Pakdaman, Morteza/0000-0002-8656-9251 | en_US |
| dc.description.abstract | The current study aims to approximate the solution of fractional differential equations (FDEs) by using the fundamental properties of artificial neural networks (ANNs) for function approximation. In the first step, we derive an approximate solution of fractional differential equation (FDE) by using ANNs. In the second step, an optimization approach is exploited to adjust the weights of ANNs such that the approximated solution satisfies the FDE. Different types of FDEs including linear and nonlinear terms are solved to illustrate the ability of the method. In addition, the present scheme is compared with the analytical solution and a number of existing numerical techniques to show the efficiency of ANNs with high accuracy, fast convergence and low use of memory for solving the FDEs. (C) 2016 Elsevier Inc. All rights reserved. | en_US |
| dc.identifier.citation | Pakdaman, M...et.al. (2017). "Solving differential equations of fractional order using an optimization technique based on training artificial neural network", Applied Mathematics And Computation, Vol.293, pp.81-95. | en_US |
| dc.identifier.doi | 10.1016/j.amc.2016.07.021 | |
| dc.identifier.issn | 0096-3003 | |
| dc.identifier.issn | 1873-5649 | |
| dc.identifier.scopus | 2-s2.0-84983508919 | |
| dc.identifier.uri | https://doi.org/10.1016/j.amc.2016.07.021 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12416/14282 | |
| dc.language.iso | en | en_US |
| dc.publisher | Elsevier Science inc | en_US |
| dc.relation.ispartof | Applied Mathematics and Computation | |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Multi-Term Fractional Differential Equations | en_US |
| dc.subject | Artificial Neural Network | en_US |
| dc.subject | Optimization | en_US |
| dc.subject | Caputo Derivative | en_US |
| dc.title | Solving Differential Equations of Fractional Order Using an Optimization Technique Based on Training Artificial Neural Network | en_US |
| dc.title | Solving differential equations of fractional order using an optimization technique based on training artificial neural network | tr_TR |
| dc.type | Article | en_US |
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| gdc.author.id | Salahshour, Soheil/0000-0003-1390-3551 | |
| gdc.author.id | Ahmadian, Ali/0000-0002-0106-7050 | |
| gdc.author.id | Effati, Sohrab/0000-0001-9752-0034 | |
| gdc.author.id | Pakdaman, Morteza/0000-0002-8656-9251 | |
| gdc.author.scopusid | 23028598900 | |
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| gdc.author.scopusid | 55959847200 | |
| gdc.author.wosid | Pakdaman, Morteza/T-8502-2019 | |
| gdc.author.wosid | Salahshour, Soheil/K-4817-2019 | |
| gdc.author.wosid | Baleanu, Dumitru/B-9936-2012 | |
| gdc.author.wosid | Ahmadian, Ali/N-3697-2015 | |
| gdc.author.wosid | Effati, Sohrab/Aaa-2991-2020 | |
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| gdc.description.department | Çankaya University | en_US |
| gdc.description.departmenttemp | [Pakdaman, M.] Islamic Azad Univ, Mashhad Branch, Young Researchers & Elite Club, Mashhad, Iran; [Ahmadian, A.] Univ Putra Malaysia, Fac Sci, Dept Math, Serdang 43400, Selangor, Malaysia; [Effati, S.] Ferdowsi Univ Mashhad, Dept Appl Math, Mashhad, Iran; [Salahshour, S.] Islamic Azad Univ, Mobarakeh Branch, Young Researchers & Elite Club, Mobarakeh, Iran; [Baleanu, D.] Cankaya Univ, Dept Math, TR-06530 Ankara, Turkey; [Baleanu, D.] Inst Space Sci, Magurele, Romania | en_US |
| gdc.description.endpage | 95 | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| gdc.description.scopusquality | Q1 | |
| gdc.description.startpage | 81 | en_US |
| gdc.description.volume | 293 | en_US |
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| gdc.oaire.keywords | multi-term fractional differential | |
| gdc.oaire.keywords | equations | |
| gdc.oaire.keywords | Fractional ordinary differential equations | |
| gdc.oaire.keywords | Neural networks for/in biological studies, artificial life and related topics | |
| gdc.oaire.keywords | Numerical methods for initial value problems involving ordinary differential equations | |
| gdc.oaire.keywords | optimization | |
| gdc.oaire.keywords | artificial neural network | |
| gdc.oaire.keywords | Caputo derivative | |
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