Titlebook: Nonlocal and Fractional Operators; Luisa Beghin,Francesco Mainardi,Roberto Garrappa Book 2021 The Editor(s) (if applicable) and The Author

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https://doi.org/10.1007/978-3-030-69236-0Fractional Calculus; Nonlocal Operators; Integro-differential Equations; Special Functions; Lèvy process

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978-3-030-69238-4The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Processes

On Time Fractional Derivatives in Fractional Sobolev Spaces and Applications to Fractional Ordinaryy are isomorphisms between the corresponding Sobolev space of order . and the .-space. On the basis of such fractional derivatives, we formulate initial value problems for time fractional ordinary differential equations and prove the well-posedness.

Thyroiditis

A Fractional Hawkes Process,We modify ETAS models by replacing the Pareto-like kernel proposed by Ogata with a Mittag-Leffler type kernel. Provided that the kernel decays as a power law with exponent ., this replacement has the advantage that the Laplace transform of the Mittag-Leffler function is known explicitly, leading to simpler calculation of relevant quantities.

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