Mathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditions

Mathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditions

Abstract The current study is devoted to deriving some results about existence and stability analysis for a nonlinear problem of implicit fractional differential equations (FODEs) with impulsive and integral boundary conditions. The concerned problem involves proportional type delay term. By using S...

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Main Authors: Arshad Ali, Kamal Shah, Thabet Abdeljawad, Ibrahim Mahariq, Mostafa Rashdan
Format: Article
Language:English
Published: SpringerOpen 2021-01-01
Series:Boundary Value Problems
Subjects:
Impulsive conditions
Proportional delay term
Stability
FODEs
Online Access:https://doi.org/10.1186/s13661-021-01484-y
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spelling doaj-1382bf9e14fa4b89b9f985daf04fa6f02021-01-17T12:56:47ZengSpringerOpenBoundary Value Problems1687-27702021-01-012021112710.1186/s13661-021-01484-yMathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditionsArshad Ali0Kamal Shah1Thabet Abdeljawad2Ibrahim Mahariq3Mostafa Rashdan4Department of Mathematics, University of Malakand ChakdaraDepartment of Mathematics, University of Malakand ChakdaraDepartment of Mathematics and General Sciences, Prince Sultan UniversityCollege of Engineering and Technology, American University of the Middle EastCollege of Engineering and Technology, American University of the Middle EastAbstract The current study is devoted to deriving some results about existence and stability analysis for a nonlinear problem of implicit fractional differential equations (FODEs) with impulsive and integral boundary conditions. The concerned problem involves proportional type delay term. By using Schaefer’s fixed point theorem and Banach’s contraction principle, the required conditions are developed. Also, different kinds of Ulam stability results are derived by using nonlinear analysis. Providing a pertinent example, we demonstrate our main results.https://doi.org/10.1186/s13661-021-01484-yImpulsive conditionsProportional delay termStabilityFODEs
collection DOAJ
language English
format Article
sources DOAJ
author Arshad Ali
Kamal Shah
Thabet Abdeljawad
Ibrahim Mahariq
Mostafa Rashdan
spellingShingle Arshad Ali
Kamal Shah
Thabet Abdeljawad
Ibrahim Mahariq
Mostafa Rashdan
Mathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditions
Boundary Value Problems
Impulsive conditions
Proportional delay term
Stability
FODEs
author_facet Arshad Ali
Kamal Shah
Thabet Abdeljawad
Ibrahim Mahariq
Mostafa Rashdan
author_sort Arshad Ali
title Mathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditions
title_short Mathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditions
title_full Mathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditions
title_fullStr Mathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditions
title_full_unstemmed Mathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditions
title_sort mathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditions
publisher SpringerOpen
series Boundary Value Problems
issn 1687-2770
publishDate 2021-01-01
description Abstract The current study is devoted to deriving some results about existence and stability analysis for a nonlinear problem of implicit fractional differential equations (FODEs) with impulsive and integral boundary conditions. The concerned problem involves proportional type delay term. By using Schaefer’s fixed point theorem and Banach’s contraction principle, the required conditions are developed. Also, different kinds of Ulam stability results are derived by using nonlinear analysis. Providing a pertinent example, we demonstrate our main results.
topic Impulsive conditions
Proportional delay term
Stability
FODEs
url https://doi.org/10.1186/s13661-021-01484-y
work_keys_str_mv AT arshadali mathematicalanalysisofnonlinearintegralboundaryvalueproblemofproportionaldelayimplicitfractionaldifferentialequationswithimpulsiveconditions
AT kamalshah mathematicalanalysisofnonlinearintegralboundaryvalueproblemofproportionaldelayimplicitfractionaldifferentialequationswithimpulsiveconditions
AT thabetabdeljawad mathematicalanalysisofnonlinearintegralboundaryvalueproblemofproportionaldelayimplicitfractionaldifferentialequationswithimpulsiveconditions
AT ibrahimmahariq mathematicalanalysisofnonlinearintegralboundaryvalueproblemofproportionaldelayimplicitfractionaldifferentialequationswithimpulsiveconditions
AT mostafarashdan mathematicalanalysisofnonlinearintegralboundaryvalueproblemofproportionaldelayimplicitfractionaldifferentialequationswithimpulsiveconditions
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