On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders

On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders

Abstract In this paper we develop the existence theory for a nonlinear Langevin equation involving Caputo fractional derivatives of different orders and Riemann–Liouville fractional integral supplemented with nonlocal multi-point and multi-strip boundary conditions. We make use of the modern methods...

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Main Authors: Bashir Ahmad, Ahmed Alsaedi, Sara Salem
Format: Article
Language:English
Published: SpringerOpen 2019-02-01
Series:Advances in Difference Equations
Online Access:http://link.springer.com/article/10.1186/s13662-019-2003-x
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spelling doaj-163a01b7d2f74837860e7af07e26d55d2020-11-25T02:26:17ZengSpringerOpenAdvances in Difference Equations1687-18472019-02-012019111410.1186/s13662-019-2003-xOn a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional ordersBashir Ahmad0Ahmed Alsaedi1Sara Salem2Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz UniversityNonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz UniversityNonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz UniversityAbstract In this paper we develop the existence theory for a nonlinear Langevin equation involving Caputo fractional derivatives of different orders and Riemann–Liouville fractional integral supplemented with nonlocal multi-point and multi-strip boundary conditions. We make use of the modern methods of functional analysis to obtain the existence and uniqueness results for the given problem, which are well illustrated with the aid of examples. Our results are new and correspond to some new ones for specific choices of the parameters involved in the problem.http://link.springer.com/article/10.1186/s13662-019-2003-x
collection DOAJ
language English
format Article
sources DOAJ
author Bashir Ahmad
Ahmed Alsaedi
Sara Salem
spellingShingle Bashir Ahmad
Ahmed Alsaedi
Sara Salem
On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders
Advances in Difference Equations
author_facet Bashir Ahmad
Ahmed Alsaedi
Sara Salem
author_sort Bashir Ahmad
title On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders
title_short On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders
title_full On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders
title_fullStr On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders
title_full_unstemmed On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders
title_sort on a nonlocal integral boundary value problem of nonlinear langevin equation with different fractional orders
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2019-02-01
description Abstract In this paper we develop the existence theory for a nonlinear Langevin equation involving Caputo fractional derivatives of different orders and Riemann–Liouville fractional integral supplemented with nonlocal multi-point and multi-strip boundary conditions. We make use of the modern methods of functional analysis to obtain the existence and uniqueness results for the given problem, which are well illustrated with the aid of examples. Our results are new and correspond to some new ones for specific choices of the parameters involved in the problem.
url http://link.springer.com/article/10.1186/s13662-019-2003-x
work_keys_str_mv AT bashirahmad onanonlocalintegralboundaryvalueproblemofnonlinearlangevinequationwithdifferentfractionalorders
AT ahmedalsaedi onanonlocalintegralboundaryvalueproblemofnonlinearlangevinequationwithdifferentfractionalorders
AT sarasalem onanonlocalintegralboundaryvalueproblemofnonlinearlangevinequationwithdifferentfractionalorders
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