A full probabilistic solution of the random linear fractional differential equation via the random variable transformation technique
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https://doi.org/10.1002/mma.4881 |
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Title
A full probabilistic solution of the random linear fractional differential equation via the random variable transformation techniqueDate
2018-11-28Publisher
John Wiley & Sons, Ltd.ISSN
0170-4214; 1099-1476Bibliographic citation
Burgos, C, Calatayud, J, Cortés, J-C, Navarro-Quiles, A. A full probabilistic solution of the random linear fractional differential equation via the random variable transformation technique. Math Meth Appl Sci. 2018; 41: 9037– 9047. https://doi.org/10.1002/mma.4881Type
info:eu-repo/semantics/articlePublisher version
https://onlinelibrary.wiley.com/doi/10.1002/mma.4881Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
This paper provides a full probabilistic solution of the randomized fractionallinear nonhomogeneous differential equation with a random initial conditionvia the computation of the first probability density function ... [+]
This paper provides a full probabilistic solution of the randomized fractionallinear nonhomogeneous differential equation with a random initial conditionvia the computation of the first probability density function of the solution sto-chastic process. To account for most generality in our analysis, we assume thatuncertainty appears in all input parameters (diffusion coefficient, source term,and initial condition) and that a wide range of probabilistic distributions can beassigned to these parameters. Throughout our study, we will consider that thefractional order of Caputo derivative lies in ]0,1], that corresponds to the mainstandard case. To conduct our analysis, we take advantage of the random var-iable transformation technique to construct approximations of the first proba-bility density function of the solution process from a suitable infinite seriesrepresentation. We then prove these approximations do converge to the exactdensity assuming mild conditions on random input parameters. Our theoreti-cal findings are illustrated through 2 numerical examples. [-]
Is part of
Mathematical Methods in the Applied Sciences, Vol. 41, Iss.18. Special Issue: Biomathematics/Advanced Analysis in Pure & Applied Sciences (Decembre 2018)Funder Name
Ministerio de Economía y Competitividad | Universitat Politècnica de València
Project code
MTM2017-89664-P | PAID-2014
Project title or grant
Programa de Ayudas de Investigación y Desarrollo (PAID)
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Copyright © 2018 John Wiley & Sons, Ltd.
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- INIT_Articles [754]