Hilbert solution, iterative algorithms, convergence theoretical results, and error bound for the fractional Langevin model arising in fluids with Caputo’s independent derivative
Studying and analyzing the random motion of a particle immersed in a liquid represented in the Langevin fractional model by Caputo’s independent derivative is one of the aims of applied physics. In this article, we will attend to a new, accurate, and comprehensive numerical solution to the aforement...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2022-12-01
|
| Series: | Frontiers in Physics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2022.1072746/full |
| _version_ | 1811200214531309568 |
|---|---|
| author | Mohammad Abdel Aal Omar Abu Arqub Banan Maayah |
| author_facet | Mohammad Abdel Aal Omar Abu Arqub Banan Maayah |
| author_sort | Mohammad Abdel Aal |
| collection | DOAJ |
| description | Studying and analyzing the random motion of a particle immersed in a liquid represented in the Langevin fractional model by Caputo’s independent derivative is one of the aims of applied physics. In this article, we will attend to a new, accurate, and comprehensive numerical solution to the aforementioned model using the reproducing kernel Hilbert approach. Basically, numerical and exact solutions of the fractional Langevin model are represented using an infinite/finite sum, simultaneously, in the Σ2Ξ space. The proof has been sketched for many mathematical theorems such as independence, convergence, error behavior, and completeness of the solution. A sufficient set of tabular results and two-dimensional graphs are shown, and absolute/relative error graphs that express the dynamic behavior of the fractional parameters α,β are utilized as well. From an analytical and practical point of view, we noticed that the simulation process and the iterative approach are appropriate, easy, and highly efficient tools for solving the studied model. In conclusion, what we have carried out is presented with a set of recommendations and an outlook on the most important literature used. |
| first_indexed | 2024-04-12T01:59:50Z |
| format | Article |
| id | doaj.art-06b090ff27b74cbe8cd9c172f732acd9 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-04-12T01:59:50Z |
| publishDate | 2022-12-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-06b090ff27b74cbe8cd9c172f732acd92022-12-22T03:52:41ZengFrontiers Media S.A.Frontiers in Physics2296-424X2022-12-011010.3389/fphy.2022.10727461072746Hilbert solution, iterative algorithms, convergence theoretical results, and error bound for the fractional Langevin model arising in fluids with Caputo’s independent derivativeMohammad Abdel Aal0Omar Abu Arqub1Banan Maayah2Department of Basic Sciences, Faculty of Arts and Educational Sciences, Middle East University, Amman, JordanDepartment of Mathematics, Faculty of Science, Al Balqa Applied University, Salt, JordanDepartment of Mathematics, Faculty of Science, The University of Jordan, Amman, JordanStudying and analyzing the random motion of a particle immersed in a liquid represented in the Langevin fractional model by Caputo’s independent derivative is one of the aims of applied physics. In this article, we will attend to a new, accurate, and comprehensive numerical solution to the aforementioned model using the reproducing kernel Hilbert approach. Basically, numerical and exact solutions of the fractional Langevin model are represented using an infinite/finite sum, simultaneously, in the Σ2Ξ space. The proof has been sketched for many mathematical theorems such as independence, convergence, error behavior, and completeness of the solution. A sufficient set of tabular results and two-dimensional graphs are shown, and absolute/relative error graphs that express the dynamic behavior of the fractional parameters α,β are utilized as well. From an analytical and practical point of view, we noticed that the simulation process and the iterative approach are appropriate, easy, and highly efficient tools for solving the studied model. In conclusion, what we have carried out is presented with a set of recommendations and an outlook on the most important literature used.https://www.frontiersin.org/articles/10.3389/fphy.2022.1072746/fullfractional Langevin modelreproducing kernel Hilbert approachfractional differential modelCaputo fractional derivative MSC202065L10fluid dynamics |
| spellingShingle | Mohammad Abdel Aal Omar Abu Arqub Banan Maayah Hilbert solution, iterative algorithms, convergence theoretical results, and error bound for the fractional Langevin model arising in fluids with Caputo’s independent derivative Frontiers in Physics fractional Langevin model reproducing kernel Hilbert approach fractional differential model Caputo fractional derivative MSC2020 65L10 fluid dynamics |
| title | Hilbert solution, iterative algorithms, convergence theoretical results, and error bound for the fractional Langevin model arising in fluids with Caputo’s independent derivative |
| title_full | Hilbert solution, iterative algorithms, convergence theoretical results, and error bound for the fractional Langevin model arising in fluids with Caputo’s independent derivative |
| title_fullStr | Hilbert solution, iterative algorithms, convergence theoretical results, and error bound for the fractional Langevin model arising in fluids with Caputo’s independent derivative |
| title_full_unstemmed | Hilbert solution, iterative algorithms, convergence theoretical results, and error bound for the fractional Langevin model arising in fluids with Caputo’s independent derivative |
| title_short | Hilbert solution, iterative algorithms, convergence theoretical results, and error bound for the fractional Langevin model arising in fluids with Caputo’s independent derivative |
| title_sort | hilbert solution iterative algorithms convergence theoretical results and error bound for the fractional langevin model arising in fluids with caputo s independent derivative |
| topic | fractional Langevin model reproducing kernel Hilbert approach fractional differential model Caputo fractional derivative MSC2020 65L10 fluid dynamics |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2022.1072746/full |
| work_keys_str_mv | AT mohammadabdelaal hilbertsolutioniterativealgorithmsconvergencetheoreticalresultsanderrorboundforthefractionallangevinmodelarisinginfluidswithcaputosindependentderivative AT omarabuarqub hilbertsolutioniterativealgorithmsconvergencetheoreticalresultsanderrorboundforthefractionallangevinmodelarisinginfluidswithcaputosindependentderivative AT bananmaayah hilbertsolutioniterativealgorithmsconvergencetheoreticalresultsanderrorboundforthefractionallangevinmodelarisinginfluidswithcaputosindependentderivative |