A boundary value problem for a random-order fractional differential equation
In this paper, we define a new Riemann–Liouville fractional integral with random order, from this Caputo and Riemann–Liouville fractional derivatives are straightforward obtained, where the fractional order of these operators is a simple random variable. We derive useful properties analogous to thos...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2022-11-01
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| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037422000528 |
| Summary: | In this paper, we define a new Riemann–Liouville fractional integral with random order, from this Caputo and Riemann–Liouville fractional derivatives are straightforward obtained, where the fractional order of these operators is a simple random variable. We derive useful properties analogous to those of the fractional operators with constant order, such as the semigroup property. As an application, we study a boundary value problem for the fractional oscillator with random order, using a random integral equation of Fredholm type. Finally, in order to solve this problem, we adapt the Nystrom method to get a numerical solution. |
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| ISSN: | 2590-0374 |