<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The aim of this paper is to study, in 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.</p></abstract>

The aim of this paper is to study, in 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.

Mean square calculus and random linear fractional differential equations: Theory and applications

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The aim of this paper is to study, in mean square sense, a class of random fractional linear differential equation where the initial condition and the forcing...

Mean square calculus and random linear fractional differential equations: Theory and applications

Published Online: Jul 28, 2017

Page range: 317 - 328

Received: Apr 04, 2017

Accepted: Jul 28, 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00026

Keywords
Random mean square Caputo derivative, random fractional linear differential equation, random Fröbenius method

© 2017 C. Burgos, J.C Cortés, L. Villafuerte, R.J. Villanueva, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mean square calculus and random linear fractional differential equations: Theory and applications

Published Online: Jul 28, 2017

Page range: 317 - 328

Received: Apr 04, 2017

Accepted: Jul 28, 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00026

KeywordsRandom mean square Caputo derivative, random fractional linear differential equation, random Fröbenius method

© 2017 C. Burgos, J.C Cortés, L. Villafuerte, R.J. Villanueva, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Random mean square Caputo derivative, random fractional linear differential equation, random Fröbenius method