A stochastic fractional calculus with applications to variational principles
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...
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| Format: | article |
| Language: | eng |
| Published: |
2020
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| Online Access: | http://hdl.handle.net/10773/28984 |
| Country: | Portugal |
| Oai: | oai:ria.ua.pt:10773/28984 |
| Summary: | 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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