Solving a class of random non-autonomous linear fractional differential equations by means of a generalized mean square convergent power series
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Other documents of the author: Burgos Simón, Clara; Calatayud, Julia; Cortés, Juan Carlos; Villafuerte, L.
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https://doi.org/10.1016/j.aml.2017.11.009 |
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Title
Solving a class of random non-autonomous linear fractional differential equations by means of a generalized mean square convergent power seriesDate
2017-11Publisher
Elsevier Ltd.ISSN
0893-9659Bibliographic citation
Burgos, C., Calatayud, J., Cortés, J. C., & Villafuerte, L. (2018). Solving a class of random non-autonomous linear fractional differential equations by means of a generalized mean square convergent power series. Applied Mathematics Letters, 78, 95-104.Type
info:eu-repo/semantics/articlePublisher version
https://www.sciencedirect.com/science/article/pii/S0893965917303464?via%3Dihub#d1e596Version
info:eu-repo/semantics/publishedVersionAbstract
The aim of this paper is to solve a class of non-autonomous linear fractional differential equations with random inputs. A mean square convergent series solution is constructed in the case that the fractional order ... [+]
The aim of this paper is to solve a class of non-autonomous linear fractional differential equations with random inputs. A mean square convergent series solution is constructed in the case that the fractional order of that Caputo derivative lies in using a random Fröbenius approach. The analysis is conducted by using the so-called mean square random calculus. The mean square convergence of the series solution is established assuming mild conditions on random inputs (diffusion coefficient and initial condition). We show that these conditions are satisfied for a variety of unbounded random variables. In addition, explicit expressions to approximate the mean, the variance and the covariance functions of the random series solution are given. Two full illustrative examples are shown. [-]
Is part of
Applied Mathematics Letters, Vol. 78 (April 2018)Funder Name
Ministerio de Economía y Competitividad
Project code
MTM2013-41765-P
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