3 research outputs found
Analytic solutions of fractional differential equations by operational methods
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
On Some Operators Involving Hadamard Derivatives
In this paper we introduce a novel Mittag--Leffler-type function and study
its properties in relation to some integro-differential operators involving
Hadamard fractional derivatives or Hyper-Bessel-type operators. We discuss then
the utility of these results to solve some integro-differential equations
involving these operators by means of operational methods. We show the
advantage of our approach through some examples. Among these, an application to
a modified Lamb--Bateman integral equation is presented