Solving random fractional second-order linear equations via the mean square Laplace transform: Theory and statistical computing

C. Burgos, J.-C. Cortés, L. Villafuerte and R.J. Villanueva

Applied Mathematics and Computation, 2022, vol. 418, issue C

Abstract: This paper deals with random fractional differential equations of the form, CD0+αX(t)+AX˙(t)+BX(t)=0, t>0, with initial conditions, X(0)=C0 and X˙(0)=C1, where CD0+αX(t) stands for the Caputo fractional derivative of X(t). We consider the case that the fractional differentiation order is 1<α<2. For the sake of generality, we further assume that C0, C1, A and B are random variables satisfying certain mild hypotheses. Then, we first construct a solution stochastic process, via a generalized power series, which is mean square convergent for all t>0. Secondly, we provide explicit approximations of the expectation and variance functions of the solution. To complete the random analysis and from this latter key information, we take advantage of the Principle of Maximum Entropy to calculate approximations of the first probability density function of the solution. All the theoretical findings are illustrated via numerical experiments.

Keywords: Random fractional differential equations; Random mean square calculus; Principle of maximum entropy; Mean square Laplace transform (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321009292

DOI: 10.1016/j.amc.2021.126846

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