Solving random fractional second-order linear equations via the mean square Laplace transform: Theory and statistical computing
作者：
Highlights：
• Random fractional second-order linear equations are probabilistically solved, under mild condition, using the Random Mean Square Calculus y the Laplace transform of a stochastic process.
• All parameters of the fractional equation are assumed to be random variables with arbitrary distributions (Full Randomization).
• The mean and the variance of the solution stochastic process are approximated.
• Several numerical examples with different probability distributions for the parameters are shown.
• The Principle of Maximum Entropy is combined together with the main statistics of the solution to determine reliable approximations of the first probability density function.
摘要
•Random fractional second-order linear equations are probabilistically solved, under mild condition, using the Random Mean Square Calculus y the Laplace transform of a stochastic process.•All parameters of the fractional equation are assumed to be random variables with arbitrary distributions (Full Randomization).•The mean and the variance of the solution stochastic process are approximated.•Several numerical examples with different probability distributions for the parameters are shown.•The Principle of Maximum Entropy is combined together with the main statistics of the solution to determine reliable approximations of the first probability density function.
论文关键词：Random fractional differential equations,Random mean square calculus,Principle of maximum entropy,Mean square Laplace transform
论文评审过程：Received 15 June 2021, Revised 29 October 2021, Accepted 28 November 2021, Available online 11 December 2021, Version of Record 11 December 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126846
