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An Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion Equations

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dc.contributor.authorZaky, M. A.
dc.contributor.authorEzz-Eldien, S. S.
dc.contributor.authorDoha, E. H.
dc.contributor.authorMachado, J. A. Tenreiro
dc.contributor.authorBhrawy, A. H.
dc.date.accessioned2017-01-25T15:46:40Z
dc.date.embargo2117
dc.date.issued2016
dc.description.abstractThis paper derives a new operational matrix of the variable-order (VO) time fractional partial derivative involved in anomalous diffusion for shifted Chebyshev polynomials. We then develop an accurate numerical algorithm to solve the 1þ1 and 2þ1 VO and constant-order fractional diffusion equation with Dirichlet conditions. The contraction of the present method is based on shifted Chebyshev collocation procedure in combination with the derived shifted Chebyshev operational matrix. The main advantage of the proposed method is to investigate a global approximation for spatial and temporal discretizations, and it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, we analyze the convergence of the present method graphically. Finally, comparisons between the algorithm derived in this paper and the existing algorithms are given, which show that our numerical schemes exhibit better performances than the existing ones.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.doi10.1115/1.4033723pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.22/9414
dc.language.isoengpt_PT
dc.publisherAmerican Society of Mechanical Engineerspt_PT
dc.relation.ispartofseriesJournal of Computational and Nonlinear Dynamics;Vol. 11, Issue 6
dc.relation.publisherversionhttp://computationalnonlinear.asmedigitalcollection.asme.org/article.aspx?articleid=2527060&resultClick=3pt_PT
dc.subjectOperational matrixpt_PT
dc.subjectCollocation methodpt_PT
dc.subjectVariable-order anomalous diffusionpt_PT
dc.subjectChebyshev polynomialspt_PT
dc.titleAn Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion Equationspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.issue6pt_PT
oaire.citation.titleJournal of Computational and Nonlinear Dynamicspt_PT
oaire.citation.volume11pt_PT
person.familyNameTenreiro Machado
person.givenNameJ. A.
person.identifier.ciencia-id7A18-4935-5B29
person.identifier.orcid0000-0003-4274-4879
person.identifier.ridM-2173-2013
person.identifier.scopus-author-id55989030100
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication82cd5c17-07b6-492b-b3e3-ecebdad1254f
relation.isAuthorOfPublication.latestForDiscovery82cd5c17-07b6-492b-b3e3-ecebdad1254f

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