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arXiv · 1706.00319

Generalised Fractional Evolution Equations of Caputo Type

M. E. Hernández-Hernández·V. N. Kolokoltsov·L. Toniazzi
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Abstract

This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations for the solutions. These results encompass known linear and non-linear equations from classical fractional partial differential equations such as the time-space-fractional diffusion equation, as well as their far reaching extensions. \\ Meaning is given to a probabilistic generalisation of Mittag-Leffler functions.

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M. E. Hernández-Hernández, V. N. Kolokoltsov, L. Toniazzi. 2017-06-01. Generalised Fractional Evolution Equations of Caputo Type. https://doi.org/10.1016/j.chaos.2017.05.005

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