Analytic solutions of fractional differential equations by operational methods
Analysis of PDEs
2013-04-04 v1
Abstract
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation of differential equations of mathematical physics. Fractionality is obtained by substituting the ordinary integer-order derivative with the Caputo fractional derivative. Furthermore, operational relations between ordinary and fractional differentiation are shown and discussed in detail. Finally, a last example concerns the application of the method to the study of a fractional Poisson process.
Keywords
Cite
@article{arxiv.1304.1056,
title = {Analytic solutions of fractional differential equations by operational methods},
author = {Roberto Garra and Federico Polito},
journal= {arXiv preprint arXiv:1304.1056},
year = {2013}
}