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 |
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Elsevier
2022-11-01
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| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037422000528 |
| _version_ | 1811188492718309376 |
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| author | Omar U. Lopez-Cresencio Francisco J. Ariza-Hernandez Jorge Sanchez-Ortiz Martin P. Arciga-Alejandre |
| author_facet | Omar U. Lopez-Cresencio Francisco J. Ariza-Hernandez Jorge Sanchez-Ortiz Martin P. Arciga-Alejandre |
| author_sort | Omar U. Lopez-Cresencio |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T14:20:45Z |
| format | Article |
| id | doaj.art-0ae5ce49cf62423f830cec23aa086421 |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-04-11T14:20:45Z |
| publishDate | 2022-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj.art-0ae5ce49cf62423f830cec23aa0864212022-12-22T04:19:04ZengElsevierResults in Applied Mathematics2590-03742022-11-0116100328A boundary value problem for a random-order fractional differential equationOmar U. Lopez-Cresencio0Francisco J. Ariza-Hernandez1Jorge Sanchez-Ortiz2Martin P. Arciga-Alejandre3Facultad de Matematicas, Universidad Autonoma de Guerrero, Av. Lazaro Cardenas S/N Cd, Universitaria, Chilpancingo, 39087, Guerrero, MexicoCorresponding authors.; Facultad de Matematicas, Universidad Autonoma de Guerrero, Av. Lazaro Cardenas S/N Cd, Universitaria, Chilpancingo, 39087, Guerrero, MexicoCorresponding authors.; Facultad de Matematicas, Universidad Autonoma de Guerrero, Av. Lazaro Cardenas S/N Cd, Universitaria, Chilpancingo, 39087, Guerrero, MexicoFacultad de Matematicas, Universidad Autonoma de Guerrero, Av. Lazaro Cardenas S/N Cd, Universitaria, Chilpancingo, 39087, Guerrero, MexicoIn 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.http://www.sciencedirect.com/science/article/pii/S2590037422000528Random order derivativeFractional oscillatorCaputo derivativeNystrom method |
| spellingShingle | Omar U. Lopez-Cresencio Francisco J. Ariza-Hernandez Jorge Sanchez-Ortiz Martin P. Arciga-Alejandre A boundary value problem for a random-order fractional differential equation Results in Applied Mathematics Random order derivative Fractional oscillator Caputo derivative Nystrom method |
| title | A boundary value problem for a random-order fractional differential equation |
| title_full | A boundary value problem for a random-order fractional differential equation |
| title_fullStr | A boundary value problem for a random-order fractional differential equation |
| title_full_unstemmed | A boundary value problem for a random-order fractional differential equation |
| title_short | A boundary value problem for a random-order fractional differential equation |
| title_sort | boundary value problem for a random order fractional differential equation |
| topic | Random order derivative Fractional oscillator Caputo derivative Nystrom method |
| url | http://www.sciencedirect.com/science/article/pii/S2590037422000528 |
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