Mean square calculus and random linear fractional differential equations: Theory and applications
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Clara Burgos Simón ; Juan Carlos Cortés López [1] ; Laura Villafuerte Altúzar [1] ; Rafael Jacinto Villanueva Micó
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[1] Universidad Politécnica de Valencia
Universidad Politécnica de Valencia
Valencia, España
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- Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 2, Nº. 2, 2017, págs. 317-328
- Idioma: inglés
- DOI: 10.21042/amns.2017.2.00001
- Texto completo no disponible (Saber más ...)
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Resumen
The aim to this paper is to study, in the mean square sense, a class of random fractional linear differential equation where the initial condition and the forcing term are assumed to be second-order random variables. The solution stochastic process of its associated Cauchy problem is constructed combining the application of a mean square chain rule for differentiating second- order stochastic processes and the random Fröbenius method. To conduct our study, first the classical Caputo derivative is extended to the random framework, in mean square sense. Furthermore, a sufficient condition to guarantee the existence of this operator is provided. Afterwards, the solution of a random fractional initial value problem is built under mild conditions. The main statistical functions of the solution stochastic process are also computed. Finally, several examples illustrate our theoretical findings.
