Mean square convergent numerical solutions of random fractional differential equations: Approximations of moments and density
[EN] A fractional forward Euler-like method is developed to solve initial value problems with uncertainties formulated via the Caputo fractional derivative. The analysis is conducted by using the so-called random mean square calculus. Under mild conditions on the data, the mean square convergence of...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/161842 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/161842 |
| Access Level: | acceso abierto |
| Palavra-chave: | Fractional differential equations with randomness Random mean square calculus Random mean square Caputo fractional derivative Random numerics Maximum Entropy Principle MATEMATICA APLICADA |
| Resumo: | [EN] A fractional forward Euler-like method is developed to solve initial value problems with uncertainties formulated via the Caputo fractional derivative. The analysis is conducted by using the so-called random mean square calculus. Under mild conditions on the data, the mean square convergence of the numerical method is proved. This type of stochastic convergence guarantees the approximations of the mean and the variance of the solution stochastic process, computed via the aforementioned numerical scheme, will converge to their corresponding exact values. Furthermore, from this probability information, we calculate reliable approximations to the first probability density function of the solution by taking advantage of the Maximum Entropy Principle. The theoretical analysis is illustrated by two examples. |
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