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

Abstract

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.

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

References in corpus (1)

• Discrete-Time Fractional Variational Problems

Cited by in corpus (1)

• A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration