Random differential operational calculus: Theory and applications

Authors:
L. Villafuerte;C. A. Braumann;J. -C. Cortés;L. Jódar
Affiliations:
Centro de Estudios en Física y Matemáticas Básicas y Aplicadas, Universidad Autónoma de Chiapas, Calle 4a Ote. Nte. 1428, Tuxtla Gutiérrez, Chiapas, Mexico;Centro de Investigação em Matemática e Aplicaçíes, Universidade de ívora, Rua Romão Ramalho 59, 7000-671, ívora, Portugal;Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Edificio 8G, 46022, Valencia, Spain;Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Edificio 8G, 46022, Valencia, Spain
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

In this article, we obtain a product rule and a chain rule for mean square derivatives. An application of the chain rule to the mean square solution of random differential equations is shown. However, to achieve such mean square differentiation rules, fourth order properties were needed and, therefore, we first studied a mean fourth order differential and integral calculus. Results are applied to solve random linear variable coefficient differential problems.