Beyond Natural Sciences
Applied Mathematics and Nonlinear Sciences

Article details
Buy now
Available online: July 28, 2017

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

Clara Burgos Simón, Juan Carlos Cortés López, Laura Villafuerte Altúzar, Rafael Jacinto Villanueva Micó
Volume 2 - Issue 2.     Year 2017.     Pages 317–328.

DOI: 10.21042/AMNS.2017.2.00026

Abstract

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.

   View all volumes & issues

Journal details

ISSN:
2444-8656
Category:
Applied Mathematics, Nonlinear Sciences

Metrics

This journal is indexed by:

This journal works looking for quality under the standards of:

© UP4, Institute of Sciences, S.L.

CIF: B-30894240
C/ Isla de la Bahía, no8, BQ 3, 4, VVDA 70,
FINCA 06813, 30868 Isla Plana (Cartagena)
(+34) 968 152055/ (+34) 600397005
info@up4sciences.org
http://www.up4sciences.org

Blog

  
Society registered at the Region of Murcia Mercantil Register issue 3111, paper 84, inscription 1 with sheet MU-88065