The analytical analysis of fractional order Fokker-Planck equations
In the current note, we broaden the utilization of a new and efficient analytical computational scheme, approximate analytical method for obtaining the solutions of fractional-order Fokker-Planck equations. The approximate solution is obtained by decomposition technique along with the property of Ri...
| Main Authors: | , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2022-04-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022665?viewType=HTML |
| _version_ | 1818201510445580288 |
|---|---|
| author | Hassan Khan Umar Farooq Fairouz Tchier Qasim Khan Gurpreet Singh Poom Kumam Kanokwan Sitthithakerngkiet |
| author_facet | Hassan Khan Umar Farooq Fairouz Tchier Qasim Khan Gurpreet Singh Poom Kumam Kanokwan Sitthithakerngkiet |
| author_sort | Hassan Khan |
| collection | DOAJ |
| description | In the current note, we broaden the utilization of a new and efficient analytical computational scheme, approximate analytical method for obtaining the solutions of fractional-order Fokker-Planck equations. The approximate solution is obtained by decomposition technique along with the property of Riemann-Liouuille fractional partial integral operator. The Caputo-Riemann operator property for fractional-order partial differential equations is calculated through the utilization of the provided initial source. This analytical scheme generates the series form solution which is fast convergent to the exact solutions. The obtained results have shown that the new technique for analytical solutions is simple to implement and very effective for analyzing the complex problems that arise in connected areas of science and technology. |
| first_indexed | 2024-12-12T02:54:42Z |
| format | Article |
| id | doaj.art-a05cc11b2daa4e0aaa4ada358484e685 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-12T02:54:42Z |
| publishDate | 2022-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-a05cc11b2daa4e0aaa4ada358484e6852022-12-22T00:40:48ZengAIMS PressAIMS Mathematics2473-69882022-04-0177119191194110.3934/math.2022665The analytical analysis of fractional order Fokker-Planck equationsHassan Khan0Umar Farooq 1Fairouz Tchier2Qasim Khan3Gurpreet Singh4Poom Kumam5Kanokwan Sitthithakerngkiet 61. Department of Mathematics, Abdul Wali khan University Mardan, Pakistan 2. Department of Mathematics, Near East University TRNC, Mersin 10, Turkey1. Department of Mathematics, Abdul Wali khan University Mardan, Pakistan3. Mathematics Department, King Saudi University, Riyadh, Saudi Arabia1. Department of Mathematics, Abdul Wali khan University Mardan, Pakistan4. School of Mathematical Sciences, Dublin City University, Ireland5. Theoretical and Computational Science (TaCS) Center, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok, Thailand 6. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan7. Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok (KMUTNB), 1518, Wongsawang, Bangsue, Bangkok 10800, ThailandIn the current note, we broaden the utilization of a new and efficient analytical computational scheme, approximate analytical method for obtaining the solutions of fractional-order Fokker-Planck equations. The approximate solution is obtained by decomposition technique along with the property of Riemann-Liouuille fractional partial integral operator. The Caputo-Riemann operator property for fractional-order partial differential equations is calculated through the utilization of the provided initial source. This analytical scheme generates the series form solution which is fast convergent to the exact solutions. The obtained results have shown that the new technique for analytical solutions is simple to implement and very effective for analyzing the complex problems that arise in connected areas of science and technology.https://www.aimspress.com/article/doi/10.3934/math.2022665?viewType=HTMLfokker-planck equationnew approximate analytical methodnonlinear fractional partial differential equationscaputo derivative operator |
| spellingShingle | Hassan Khan Umar Farooq Fairouz Tchier Qasim Khan Gurpreet Singh Poom Kumam Kanokwan Sitthithakerngkiet The analytical analysis of fractional order Fokker-Planck equations AIMS Mathematics fokker-planck equation new approximate analytical method nonlinear fractional partial differential equations caputo derivative operator |
| title | The analytical analysis of fractional order Fokker-Planck equations |
| title_full | The analytical analysis of fractional order Fokker-Planck equations |
| title_fullStr | The analytical analysis of fractional order Fokker-Planck equations |
| title_full_unstemmed | The analytical analysis of fractional order Fokker-Planck equations |
| title_short | The analytical analysis of fractional order Fokker-Planck equations |
| title_sort | analytical analysis of fractional order fokker planck equations |
| topic | fokker-planck equation new approximate analytical method nonlinear fractional partial differential equations caputo derivative operator |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022665?viewType=HTML |
| work_keys_str_mv | AT hassankhan theanalyticalanalysisoffractionalorderfokkerplanckequations AT umarfarooq theanalyticalanalysisoffractionalorderfokkerplanckequations AT fairouztchier theanalyticalanalysisoffractionalorderfokkerplanckequations AT qasimkhan theanalyticalanalysisoffractionalorderfokkerplanckequations AT gurpreetsingh theanalyticalanalysisoffractionalorderfokkerplanckequations AT poomkumam theanalyticalanalysisoffractionalorderfokkerplanckequations AT kanokwansitthithakerngkiet theanalyticalanalysisoffractionalorderfokkerplanckequations AT hassankhan analyticalanalysisoffractionalorderfokkerplanckequations AT umarfarooq analyticalanalysisoffractionalorderfokkerplanckequations AT fairouztchier analyticalanalysisoffractionalorderfokkerplanckequations AT qasimkhan analyticalanalysisoffractionalorderfokkerplanckequations AT gurpreetsingh analyticalanalysisoffractionalorderfokkerplanckequations AT poomkumam analyticalanalysisoffractionalorderfokkerplanckequations AT kanokwansitthithakerngkiet analyticalanalysisoffractionalorderfokkerplanckequations |