Nonlinear Langevin equations and inclusions involving mixed fractional order derivatives and variable coefficient with fractional nonlocal-terminal conditions
In this paper, we discuss the existence and uniqueness of solutions for a new kind of Langevin equation involving Riemann-Liouville as well as Caputo fractional derivatives, and variable coefficient, supplemented with nonlocal-terminal fractional integro-differential conditions. The proposed study i...
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| Format: | Article |
| Language: | English |
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AIMS Press
2019-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2019.3.626/fulltext.html |
| _version_ | 1828181269335244800 |
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| author | Bashir Ahmad Ahmed Alsaedi Sotiris K. Ntouyas |
| author_facet | Bashir Ahmad Ahmed Alsaedi Sotiris K. Ntouyas |
| author_sort | Bashir Ahmad |
| collection | DOAJ |
| description | In this paper, we discuss the existence and uniqueness of solutions for a new kind of Langevin equation involving Riemann-Liouville as well as Caputo fractional derivatives, and variable coefficient, supplemented with nonlocal-terminal fractional integro-differential conditions. The proposed study is based on modern tools of functional analysis. We also extend our discussion to the associated inclusions problem. For the applicability of the obtained results, several examples are constructed. Some interesting observations are also presented. |
| first_indexed | 2024-04-12T06:00:36Z |
| format | Article |
| id | doaj.art-993c0f958c3a4eff8a3785d7bd8aa966 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-12T06:00:36Z |
| publishDate | 2019-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-993c0f958c3a4eff8a3785d7bd8aa9662022-12-22T03:45:03ZengAIMS PressAIMS Mathematics2473-69882019-06-014362664710.3934/math.2019.3.626Nonlinear Langevin equations and inclusions involving mixed fractional order derivatives and variable coefficient with fractional nonlocal-terminal conditionsBashir Ahmad0Ahmed Alsaedi1Sotiris K. Ntouyas21 Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia1 Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia1 Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia 2 Department of Mathematics, University of Ioannina, 451 10 Ioannina, GreeceIn this paper, we discuss the existence and uniqueness of solutions for a new kind of Langevin equation involving Riemann-Liouville as well as Caputo fractional derivatives, and variable coefficient, supplemented with nonlocal-terminal fractional integro-differential conditions. The proposed study is based on modern tools of functional analysis. We also extend our discussion to the associated inclusions problem. For the applicability of the obtained results, several examples are constructed. Some interesting observations are also presented.https://www.aimspress.com/article/10.3934/math.2019.3.626/fulltext.htmlfractional derivativesfractional integralLangevin equationsnonlocal-terminal value problemsexistenceuniquenessfixed point theorems |
| spellingShingle | Bashir Ahmad Ahmed Alsaedi Sotiris K. Ntouyas Nonlinear Langevin equations and inclusions involving mixed fractional order derivatives and variable coefficient with fractional nonlocal-terminal conditions AIMS Mathematics fractional derivatives fractional integral Langevin equations nonlocal-terminal value problems existence uniqueness fixed point theorems |
| title | Nonlinear Langevin equations and inclusions involving mixed fractional order derivatives and variable coefficient with fractional nonlocal-terminal conditions |
| title_full | Nonlinear Langevin equations and inclusions involving mixed fractional order derivatives and variable coefficient with fractional nonlocal-terminal conditions |
| title_fullStr | Nonlinear Langevin equations and inclusions involving mixed fractional order derivatives and variable coefficient with fractional nonlocal-terminal conditions |
| title_full_unstemmed | Nonlinear Langevin equations and inclusions involving mixed fractional order derivatives and variable coefficient with fractional nonlocal-terminal conditions |
| title_short | Nonlinear Langevin equations and inclusions involving mixed fractional order derivatives and variable coefficient with fractional nonlocal-terminal conditions |
| title_sort | nonlinear langevin equations and inclusions involving mixed fractional order derivatives and variable coefficient with fractional nonlocal terminal conditions |
| topic | fractional derivatives fractional integral Langevin equations nonlocal-terminal value problems existence uniqueness fixed point theorems |
| url | https://www.aimspress.com/article/10.3934/math.2019.3.626/fulltext.html |
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