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. © 2012 Elsevier Inc. All rights reserved.

Analytic solutions of fractional differential equations by operational methods / Garra, Roberto; Polito, Federico. - In: APPLIED MATHEMATICS AND COMPUTATION. - ISSN 0096-3003. - 218:21(2012), pp. 10642-10646. [10.1016/j.amc.2012.04.028]

Analytic solutions of fractional differential equations by operational methods

GARRA, ROBERTO;POLITO, FEDERICO
2012

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. © 2012 Elsevier Inc. All rights reserved.
2012
fractional differential equations; fractional diffusion; fractional poisson process; mittag-leffler functions; operational methods
01 Pubblicazione su rivista::01a Articolo in rivista
Analytic solutions of fractional differential equations by operational methods / Garra, Roberto; Polito, Federico. - In: APPLIED MATHEMATICS AND COMPUTATION. - ISSN 0096-3003. - 218:21(2012), pp. 10642-10646. [10.1016/j.amc.2012.04.028]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/511324
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