Fractional relaxation equations, as well as relaxation functions time-changed by independent stochastic processes have been widely studied (see, for example, MAI, STAW and GAR). We start here by proving that the upper-incomplete Gamma function satisfies the tempered-relaxation equation (of index ρ∈(0,1)); thanks to this explicit form of the solution, we can then derive its spectral distribution, which extends the stable law. Accordingly, we define a new class of selfsimilar processes (by means of the n-times Laplace transform of its density) which is indexed by the parameter ρ: in the special case where ρ=1, it reduces to the stable subordinator. Therefore the parameter ρ can be seen as a measure of the local deviation from the temporal dependence structure displayed in the standard stable case.
TEMPERED RELAXATION EQUATION AND RELATED GENERALIZED STABLE PROCESSES / Beghin, L.; Gajda, J.. - In: FRACTIONAL CALCULUS & APPLIED ANALYSIS. - ISSN 1314-2224. - 23:5(2020), pp. 1248-1273.
|Titolo:||TEMPERED RELAXATION EQUATION AND RELATED GENERALIZED STABLE PROCESSES|
BEGHIN, Luisa (Primo) (Corresponding author)
|Data di pubblicazione:||2020|
|Citazione:||TEMPERED RELAXATION EQUATION AND RELATED GENERALIZED STABLE PROCESSES / Beghin, L.; Gajda, J.. - In: FRACTIONAL CALCULUS & APPLIED ANALYSIS. - ISSN 1314-2224. - 23:5(2020), pp. 1248-1273.|
|Appartiene alla tipologia:||01a Articolo in rivista|