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 |
Keywords:
anomalous relaxation; completely monotone functions; fractional derivative; spectral distributions; Mittag-Leffler functionsSoftware:
Kilbas SaigoReferences:
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