Journal
APPLIED MATHEMATICS LETTERS
Volume 22, Issue 3, Pages 378-385Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2008.06.003
Keywords
Fractional calculus; Modified Riemann-Liouville derivative; Fractional Taylor's series; Mittag-Leffler function
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In order to cope with some difficulties due to the fact that the derivative of a constant is not zero with the commonly accepted Riemann-Liouvile definition of fractional derivatives, one (Jumarie) has proposed recently an alternative referred to as a modified Riemann-Liouville definition, which directly, provides a Taylor's series of fractional order for non differentiable functions. This fractional derivative provides a fractional calculus parallel with the classical one, which applies to non-differentiable functions: and the present short article summarizes the main basic formulae so obtained. (C) 2008 Elsevier Ltd. All rights reserved.
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