Speaker
Description
In this talk we give an explicit solution to Dzherbashyan-Caputo-fractional Cauchy problems related to equations with derivatives of order $\nu_k$, for $k$ non-negative integer and $\nu > 0$. The solution is obtained by connecting the differential equation with the roots of the characteristic polynomial and it is expressed in terms of Mittag-Leffler-type functions. Under some additional hypothesis, the solution can be expressed as a linear combination of Mittag-Leffler functions with common fractional order $\nu$. We establish a probabilistic relationship, involving the inverse of stable subordinator, between the solutions of differential problems with order $\alpha_\nu$ and $\nu$, for $\alpha\in (0, 1)$.
Finally, we use the described method to solve fractional differential equations arising in the fractionalization of partial differential equations related to the probability law of planar random motions with finite velocities.
