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Stable numerical results to a class of time-space fractional partial differential equations via spectral method

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dc.contributor.author Shah, Kamal
dc.contributor.author Jarad, Fahd
dc.contributor.author Abdeljawad, Thabet
dc.date.accessioned 2020-12-24T12:34:46Z
dc.date.available 2020-12-24T12:34:46Z
dc.date.issued 2020-09
dc.identifier.citation Shah, Kamal; Jarad, Fahd; Abdeljawad, Thabet (2020). "Stable numerical results to a class of time-space fractional partial differential equations via spectral method", Journal of Advanced Research, Vol. 25, No. Special Issue, pp. 39-48. tr_TR
dc.identifier.issn 2090-1232
dc.identifier.issn 2090-1224
dc.identifier.uri http://hdl.handle.net/20.500.12416/4389
dc.description.abstract In this paper, we are concerned with finding numerical solutions to the class of time-space fractional partial differential equations: D(t)(p)u(t, x) + kappa D(x)(p)u(t, x) + tau u(t, x) = g(t, x), 1 < p < 2, (t, x) is an element of [0,1] x [0, 1], under the initial conditions. u(0, x) = theta(x), u(t)(0, x) = phi(x), and the mixed boundary conditions. u(t, 0) = u(x)(t, 0) = 0, where D-t(p) is the arbitrary derivative in Caputo sense of order p corresponding to the variable time t. Further, D-x(p) is the arbitrary derivative in Caputo sense with order p corresponding to the variable space x. Using shifted Jacobin polynomial basis and via some operational matrices of fractional order integration and differentiation, the considered problem is reduced to solve a system of linear equations. The used method doesn't need discretization. A test problem is presented in order to validate the method. Moreover, it is shown by some numerical tests that the suggested method is stable with respect to a small perturbation of the source data g(t, x). Further the exact and numerical solutions are compared via 3D graphs which shows that both the solutions coincides very well. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University. tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.1016/j.jare.2020.05.022 tr_TR
dc.rights info:eu-repo/semantics/openAccess tr_TR
dc.subject Fractional Partial Differential Equations tr_TR
dc.subject Caputo Fractional Derivative tr_TR
dc.subject Shifted Jacobin Polynomials tr_TR
dc.subject Operational Matrices tr_TR
dc.subject Numerical Solution tr_TR
dc.subject Stability tr_TR
dc.title Stable numerical results to a class of time-space fractional partial differential equations via spectral method tr_TR
dc.type article tr_TR
dc.relation.journal Journal of Advanced Research tr_TR
dc.contributor.authorID 234808 tr_TR
dc.identifier.volume 25 tr_TR
dc.identifier.issue Special Issue tr_TR
dc.identifier.startpage 39 tr_TR
dc.identifier.endpage 48 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü tr_TR


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