Matrix approach to discrete fractional calculus II: partial fractional differential equations

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dc.creatorPodlubny, Igor
dc.creatorChechkin, Aleksei V.
dc.creatorSkovranek, Tomas
dc.creatorChen, YangQuan
dc.creatorJara, Blas M. Vinagre
dc.date2008-11-09
dc.date2009-01-14
dc.date.accessioned2026-07-07T12:49:10Z
dc.date.available2026-07-07T12:49:10Z
dc.descriptionA new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested method is the development of Podlubny's matrix approach (Fractional Calculus and Applied Analysis, vol. 3, no. 4, 2000, 359--386). Four examples of numerical solution of fractional diffusion equation with various combinations of time/space fractional derivatives (integer/integer, fractional/integer, integer/fractional, and fractional/fractional) with respect to time and to the spatial variable are provided in order to illustrate how simple and general is the suggested approach. The fifth example illustrates that the method can be equally simply used for fractional differential equations with delays. A set of MATLAB routines for the implementation of the method as well as sample code used to solve the examples have been developed.
dc.description33 pages, 12 figures
dc.identifierhttps://arxiv.org/abs/0811.1355
dc.identifierhttp://arxiv.org/abs/0811.1355
dc.identifierJournal of Computational Physics, vol. 228, no. 8, 1 May 2009, pp. 3137-3153
dc.identifierdoi:10.1016/j.jcp.2009.01.014
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222310
dc.subjectNumerical Analysis
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.subjectComputational Physics
dc.subject26A33; 65M06; 91B82; 65Z05; 65D25
dc.titleMatrix approach to discrete fractional calculus II: partial fractional differential equations
dc.typetext

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