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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Acknowledgements
This work has been supported by the Spanish Ministerio de Economía, Industria y Competitividad (MINECO), the Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE) grant MTM2017-89664-P. Computations have been carried thanks to the collaboration of Raúl San Julián Garcés and Elena López Navarro granted by European Union through the Operational Program of the European Regional Development Fund (ERDF)/European Social Fund (ESF) of the Valencian Community 2014–2020, grants GJIDI/2018/A/009 and GJIDI/2018/A/010, respectively.
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Burgos, C., Cortés, JC., Roselló, MD., Villanueva, RJ. (2021). Some Tools to Study Random Fractional Differential Equations and Applications. In: De Cursi, J. (eds) Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling. Uncertainties 2020. Lecture Notes in Mechanical Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-030-53669-5_2
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