Momani, Shaher; Rqayiq, Abdullah Abu; Baleanu, Dumitru A nonstandard finite difference scheme for two-sided space-fractional partial differential equations. (English) Zbl 1258.35201 Int. J. Bifurcation Chaos Appl. Sci. Eng. 22, No. 4, Paper No. 1250079, 5 p. (2012). Summary: We apply the Mickens nonstandard discretization method to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain, and thereby increase the accuracy of the solutions. We examine the case when a left-handed and a right-handed fractional spatial derivative may be present in the partial differential equation. Two numerical examples using this method are presented and compared successfully with the exact analytical solutions. Cited in 15 Documents MSC: 35R11 Fractional partial differential equations 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs Keywords:fractional differential equations; left-handed fractional derivative; right-handed fractional derivative; nonstandard finite difference schemes PDFBibTeX XMLCite \textit{S. Momani} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 22, No. 4, Paper No. 1250079, 5 p. (2012; Zbl 1258.35201) Full Text: DOI References: [1] DOI: 10.1016/j.cam.2009.09.027 · Zbl 1185.65146 [2] DOI: 10.1007/978-3-0348-8291-0_17 [3] DOI: 10.1016/j.cam.2004.01.033 · Zbl 1126.76346 [4] DOI: 10.1016/j.apnum.2005.02.008 · Zbl 1086.65087 [5] DOI: 10.1002/num.1690050404 · Zbl 0693.65059 [6] DOI: 10.1016/0016-0032(90)90062-N · Zbl 0695.93063 [7] Mickens R., Nonstandard Finite-Difference Models of Differential Equations (1994) · Zbl 0810.65083 [8] Mickens R., Numer. Meth. Partial Diff. Eqs. 15 pp 202– [9] DOI: 10.1006/jsvi.2001.3783 · Zbl 1237.65084 [10] DOI: 10.1006/jsvi.2001.4240 · Zbl 1237.65095 [11] DOI: 10.1016/S0378-4754(02)00180-5 · Zbl 1015.65036 [12] Miller K., An Introduction to the Fractional Calculus and Fractional Differential Equations (1993) · Zbl 0789.26002 [13] Oldham K. B., The Fractional Calculus (1974) · Zbl 0292.26011 [14] Podlubny I., Fractional Differential Equations (1999) · Zbl 0924.34008 [15] Samko S., Fractional Integral and Derivatives: Theory and Applications (1993) [16] DOI: 10.1016/j.jcp.2005.08.008 · Zbl 1089.65089 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.