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arXiv · 2008.00233

A Stochastic Fractional Calculus with Applications to Variational Principles

Houssine Zine·Delfim F. M. Torres
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Abstract

We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional Euler-Lagrange equation is obtained, extending those available in the literature for the classical, fractional, and stochastic calculus of variations. To illustrate our main theoretical result, we discuss two examples: one derived from quantum mechanics, the second validated by an adequate numerical simulation.

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Houssine Zine, Delfim F. M. Torres. 2020-08-01. A Stochastic Fractional Calculus with Applications to Variational Principles. https://doi.org/10.3390/fractalfract4030038

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