Analysis of the Fractional Differential Equations Using Two Different Methods

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dc.authoridde la Sen, manuel/0000-0001-9320-9433
dc.contributor.authorPartohaghighi, Mohammad
dc.contributor.authorAkgul, Ali
dc.contributor.authorAkgul, Esra Karatas
dc.contributor.authorAttia, Nourhane
dc.contributor.authorDe la Sen, Manuel
dc.contributor.authorBayram, Mustafa
dc.date.accessioned2024-12-24T19:33:46Z
dc.date.available2024-12-24T19:33:46Z
dc.date.issued2023
dc.departmentSiirt Üniversitesi
dc.description.abstractNumerical methods play an important role in modern mathematical research, especially studying the symmetry analysis and obtaining the numerical solutions of fractional differential equation. In the current work, we use two numerical schemes to deal with fractional differential equations. In the first case, a combination of the group preserving scheme and fictitious time integration method (FTIM) is considered to solve the problem. Firstly, we applied the FTIM role, and then the GPS came to integrate the obtained new system using initial conditions. Figure and tables containing the solutions are provided. The tabulated numerical simulations are compared with the reproducing kernel Hilbert space method (RKHSM) as well as the exact solution. The methodology of RKHSM mainly relies on the right choice of the reproducing kernel functions. The results confirm that the FTIM finds the true solution. Additionally, these numerical results indicate the effectiveness of the proposed methods.
dc.identifier.doi10.3390/sym15010065
dc.identifier.issn2073-8994
dc.identifier.issue1
dc.identifier.scopus2-s2.0-85146739762
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.3390/sym15010065
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8286
dc.identifier.volume15
dc.identifier.wosWOS:000916205900001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofSymmetry-Basel
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectfictitious time integration method
dc.subjecttime-fractional heat equation
dc.subjectfractional differential equations
dc.subjectreproducing kernel Hilbert space method
dc.subjectgroup-preserving scheme
dc.titleAnalysis of the Fractional Differential Equations Using Two Different Methods
dc.typeArticle

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