Fractional models of anomalous relaxation based on the Kilbas and Saigo function.(English)Zbl 1307.34007

From the summary: After some remarks on the Kilbas and Saigo functions, we discuss a class of fractional differential equations of order $$\alpha \in (0,1]$$ with a characteristic coefficient varying in time according to a power law of exponent $$\beta$$, whose solutions will be presented in terms of these functions. We show 2D plots of the solutions and, for a few of them, the corresponding spectral distributions, keeping fixed one of the two order-parameters. The numerical results confirm the complete monotonicity of the solutions via the non-negativity of the spectral distributions, provided that the parameters satisfy the additional condition $$0<\alpha +\beta \leq 1$$, assumed by us.

MSC:

 34A08 Fractional ordinary differential equations 33E12 Mittag-Leffler functions and generalizations

Kilbas Saigo
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References:

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