Fractional Derivatives and Integrals on Time Scales via the Inverse Generalized Laplace Transform

Details Fractional Derivatives and Integrals on Time Scales via the Inverse Generalized Laplace Transform Fractional Derivatives and Integrals on Time Scales via the Inverse Generalized Laplace Transform

2010-12-07

arxiv.org/abs/1012.1555v1

Int. J. Math. Comput. 11 (2011), no. J11, 1--9

Mathematics

Classical Analysis and ODEs

Submitted 20-Aug-2010; accepted 11-Nov-2010. Ref: Int. J. Math. Comput. 11 (2011), no. J11, 1--9

Scientific paper

We introduce a fractional calculus on time scales using the theory of delta
(or nabla) dynamic equations. The basic notions of fractional order integral
and fractional order derivative on an arbitrary time scale are proposed, using
the inverse Laplace transform on time scales. Useful properties of the new
fractional operators are proved.

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