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2021 | OriginalPaper | Chapter

Some Tools to Study Random Fractional Differential Equations and Applications

Authors : Clara Burgos, Juan-Carlos Cortés, María-Dolores Roselló, Rafael-J. Villanueva

Published in: Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling

Publisher: Springer International Publishing

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Abstract

Random fractional differential equations are useful mathematical tools to model problems involving memory effects and uncertainties. In this contribution, we present some results, which extent their deterministic counterpart, to fractional differential equations whose initial conditions and coefficients are random variables and/or stochastic process. The probabilistic analysis utilizes the random mean square calculus. For the sake of completeness, we study both autonomous and non-autonomous initial value problems. The analysis includes the computation of analytical and numerical solutions, as well as their main probabilistic information such as the mean, the variance and the first probability density function. Several examples illustrating the theoretical results are shown.

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Metadata
Title
Some Tools to Study Random Fractional Differential Equations and Applications
Authors
Clara Burgos
Juan-Carlos Cortés
María-Dolores Roselló
Rafael-J. Villanueva
Copyright Year
2021
Book
Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling

Print ISBN: 978-3-030-53668-8

Electronic ISBN: 978-3-030-53669-5

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-53669-5_2