2,452 research outputs found
From Sturm-Liouville problems to fractional and anomalous diffusions
Some fractional and anomalous diffusions are driven by equations involving
fractional derivatives in both time and space. Such diffusions are processes
with randomly varying times. In representing the solutions to those diffusions,
the explicit laws of certain stable processes turn out to be fundamental. This
paper directs one's efforts towards the explicit representation of solutions to
fractional and anomalous diffusions related to Sturm-Liouville problems of
fractional order associated to fractional power function spaces. Furthermore,
we study a new version of the Bochner's subordination rule and we establish
some connections between subordination and space-fractional operatorComment: Accepted by Stochastic Processess and Their Application
Fractional Diffusion-Telegraph Equations and their Associated Stochastic Solutions
We present the stochastic solution to a generalized fractional partial
differential equation involving a regularized operator related to the so-called
Prabhakar operator and admitting, amongst others, as specific cases the
fractional diffusion equation and the fractional telegraph equation. The
stochastic solution is expressed as a L\'evy process time-changed with the
inverse process to a linear combination of (possibly subordinated) independent
stable subordinators of different indices. Furthermore a related SDE is derived
and discussed
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