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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2010
- DOI:
- 10.48550/arXiv.1012.1555
- arXiv:
- arXiv:1012.1555
- Bibcode:
- 2010arXiv1012.1555B
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- 26A33;
- 26E70;
- 44A10
- E-Print:
- Submitted 20-Aug-2010