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Solving differential equations of fractional order using an optimization technique based on training artificial neural network

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dc.contributor.author Pakdaman, M.
dc.contributor.author Ahmadian, Ali
dc.contributor.author Effati, S.
dc.contributor.author Salahshour, S.
dc.contributor.author Baleanu, Dumitru
dc.date.accessioned 2020-03-19T11:56:25Z
dc.date.available 2020-03-19T11:56:25Z
dc.date.issued 2017-01-15
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. tr_TR
dc.identifier.issn 0096-3003
dc.identifier.uri http://hdl.handle.net/20.500.12416/2692
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. tr_TR
dc.language.iso eng tr_TR
dc.publisher Elsevier Science INC tr_TR
dc.relation.isversionof 10.1016/j.amc.2016.07.021 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Multi-Term Fractional Differential Equations tr_TR
dc.subject Artificial Neural Network tr_TR
dc.subject Optimization tr_TR
dc.subject Caputo Derivative tr_TR
dc.title Solving differential equations of fractional order using an optimization technique based on training artificial neural network tr_TR
dc.type article tr_TR
dc.relation.journal Applied Mathematics And Computation tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 293 tr_TR
dc.identifier.startpage 81 tr_TR
dc.identifier.endpage 95 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü tr_TR


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