×

How to approximate the fractional derivative of order \(1 < \alpha \leq 2\). (English) Zbl 1258.26006


MSC:

26A33 Fractional derivatives and integrals
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65L12 Finite difference and finite volume methods for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Abramowitz M., Handbook of Mathematical Functions (1970)
[2] DOI: 10.1029/2000WR900031
[3] DOI: 10.1023/B:NUMA.0000027736.85078.be · Zbl 1055.65098
[4] DOI: 10.1016/j.jconhyd.2005.12.007
[5] DOI: 10.1016/j.camwa.2006.02.001 · Zbl 1137.65001
[6] Kilbas A. A., Theory and Applications of Fractional Differential Equations (2006) · Zbl 1138.26300
[7] DOI: 10.1016/j.camwa.2009.07.050 · Zbl 1189.65142
[8] DOI: 10.1016/j.jcp.2011.01.030 · Zbl 1218.65070
[9] DOI: 10.1137/0517050 · Zbl 0624.65015
[10] DOI: 10.1016/j.cam.2004.01.033 · Zbl 1126.76346
[11] Oldham K. B., The Fractional Calculus (1974) · Zbl 0292.26011
[12] Pachepsky Y., Soil Sci. Soc. Am. J. 4 pp 1234–
[13] Podlubny I., Fractional Differential Equations (1999) · Zbl 0924.34008
[14] Samko S. G., Fractional Integrals and Derivatives: Theory and Applications (1993) · Zbl 0818.26003
[15] Shen S., ANZIAM J. 46 pp C871–
[16] DOI: 10.1016/j.jcp.2009.02.011 · Zbl 1169.65126
[17] DOI: 10.1016/j.camwa.2011.04.015 · Zbl 1228.65153
[18] DOI: 10.1016/j.jcp.2005.08.008 · Zbl 1089.65089
[19] DOI: 10.1137/030602666 · Zbl 1119.65379
[20] DOI: 10.1016/S0370-1573(02)00331-9 · Zbl 0999.82053
[21] DOI: 10.1016/j.advwatres.2006.11.002
[22] DOI: 10.2136/sssaj2003.1079
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.