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Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative

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dc.contributor.author Arshad, Sadia
dc.contributor.author Baleanu, Dumitru
dc.contributor.author Huang, Jianfei
dc.contributor.author Al Qurashi, Maysaa Mohamed
dc.contributor.author Tang, Yifa
dc.contributor.author Zhao, Yue
dc.date.accessioned 2019-12-20T12:35:35Z
dc.date.available 2019-12-20T12:35:35Z
dc.date.issued 2018-05
dc.identifier.citation Arshad, Sadia...et al. (2018). Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative, Entropy, 20(5). tr_TR
dc.identifier.issn 1099-4300
dc.identifier.uri http://hdl.handle.net/20.500.12416/2212
dc.description.abstract In this article, a numerical scheme is formulated and analysed to solve the time-space fractional advection-diffusion equation, where the Riesz derivative and the Caputo derivative are considered in spatial and temporal directions, respectively. The Riesz space derivative is approximated by the second-order fractional weighted and shifted Grunwald-Letnikov formula. Based on the equivalence between the fractional differential equation and the integral equation, we have transformed the fractional differential equation into an equivalent integral equation. Then, the integral is approximated by the trapezoidal formula. Further, the stability and convergence analysis are discussed rigorously. The resulting scheme is formally proved with the second order accuracy both in space and time. Numerical experiments are also presented to verify the theoretical analysis. tr_TR
dc.language.iso eng tr_TR
dc.publisher MDPI tr_TR
dc.relation.isversionof 10.3390/e20050321 tr_TR
dc.rights info:eu-repo/semantics/openAccess tr_TR
dc.subject Fractional Advection Dispersion Equation tr_TR
dc.subject Riesz Derivative tr_TR
dc.subject Caputo Derivative tr_TR
dc.subject Trapezoidal Formula tr_TR
dc.title Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative tr_TR
dc.type article tr_TR
dc.relation.journal Entropy tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 20 tr_TR
dc.identifier.issue 5 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik - Bilgisayar Bölümü tr_TR


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