Generalised Fractional Evolution Equations of Caputo Type
Analysis of PDEs
2022-05-03 v1
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.
Cite
@article{arxiv.1706.00319,
title = {Generalised Fractional Evolution Equations of Caputo Type},
author = {M. E. Hernández-Hernández and V. N. Kolokoltsov and L. Toniazzi},
journal= {arXiv preprint arXiv:1706.00319},
year = {2022}
}
Comments
To be published in 'Chaos, Solitons & Fractals'