Mathematical Analysis of Nonlocal Implicit Impulsive Problem under Caputo Fractional Boundary Conditions

Mathematical Analysis of Nonlocal Implicit Impulsive Problem under Caputo Fractional Boundary Conditions

This paper is related to frame a mathematical analysis of impulsive fractional order differential equations (IFODEs) under nonlocal Caputo fractional boundary conditions (NCFBCs). By using fixed point theorems of Schaefer and Banach, we analyze the existence and uniqueness results for the considered...

Full description

Bibliographic Details
Main Authors: Arshad Ali, Vidushi Gupta, Thabet Abdeljawad, Kamal Shah, Fahd Jarad
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2020/7681479
id doaj-68f1360c636b4a08bfdd5bd19f75bbf8
record_format Article
spelling doaj-68f1360c636b4a08bfdd5bd19f75bbf82020-12-14T09:46:38ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472020-01-01202010.1155/2020/76814797681479Mathematical Analysis of Nonlocal Implicit Impulsive Problem under Caputo Fractional Boundary ConditionsArshad Ali0Vidushi Gupta1Thabet Abdeljawad2Kamal Shah3Fahd Jarad4Department of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, Chandigarh University, Chandigarh, Punjab, IndiaDepartment of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi ArabiaDepartment of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, Cankaya University, Ankara, TurkeyThis paper is related to frame a mathematical analysis of impulsive fractional order differential equations (IFODEs) under nonlocal Caputo fractional boundary conditions (NCFBCs). By using fixed point theorems of Schaefer and Banach, we analyze the existence and uniqueness results for the considered problem. Furthermore, we utilize the theory of stability for presenting Hyers-Ulam, generalized Hyers-Ulam, Hyers-Ulam-Rassias, and generalized Hyers-Ulam-Rassias stability results of the proposed scheme. Finally, some applications are offered to demonstrate the concept and results. The whole analysis is carried out by using Caputo fractional derivatives (CFDs).http://dx.doi.org/10.1155/2020/7681479
collection DOAJ
language English
format Article
sources DOAJ
author Arshad Ali
Vidushi Gupta
Thabet Abdeljawad
Kamal Shah
Fahd Jarad
spellingShingle Arshad Ali
Vidushi Gupta
Thabet Abdeljawad
Kamal Shah
Fahd Jarad
Mathematical Analysis of Nonlocal Implicit Impulsive Problem under Caputo Fractional Boundary Conditions
Mathematical Problems in Engineering
author_facet Arshad Ali
Vidushi Gupta
Thabet Abdeljawad
Kamal Shah
Fahd Jarad
author_sort Arshad Ali
title Mathematical Analysis of Nonlocal Implicit Impulsive Problem under Caputo Fractional Boundary Conditions
title_short Mathematical Analysis of Nonlocal Implicit Impulsive Problem under Caputo Fractional Boundary Conditions
title_full Mathematical Analysis of Nonlocal Implicit Impulsive Problem under Caputo Fractional Boundary Conditions
title_fullStr Mathematical Analysis of Nonlocal Implicit Impulsive Problem under Caputo Fractional Boundary Conditions
title_full_unstemmed Mathematical Analysis of Nonlocal Implicit Impulsive Problem under Caputo Fractional Boundary Conditions
title_sort mathematical analysis of nonlocal implicit impulsive problem under caputo fractional boundary conditions
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2020-01-01
description This paper is related to frame a mathematical analysis of impulsive fractional order differential equations (IFODEs) under nonlocal Caputo fractional boundary conditions (NCFBCs). By using fixed point theorems of Schaefer and Banach, we analyze the existence and uniqueness results for the considered problem. Furthermore, we utilize the theory of stability for presenting Hyers-Ulam, generalized Hyers-Ulam, Hyers-Ulam-Rassias, and generalized Hyers-Ulam-Rassias stability results of the proposed scheme. Finally, some applications are offered to demonstrate the concept and results. The whole analysis is carried out by using Caputo fractional derivatives (CFDs).
url http://dx.doi.org/10.1155/2020/7681479
work_keys_str_mv AT arshadali mathematicalanalysisofnonlocalimplicitimpulsiveproblemundercaputofractionalboundaryconditions
AT vidushigupta mathematicalanalysisofnonlocalimplicitimpulsiveproblemundercaputofractionalboundaryconditions
AT thabetabdeljawad mathematicalanalysisofnonlocalimplicitimpulsiveproblemundercaputofractionalboundaryconditions
AT kamalshah mathematicalanalysisofnonlocalimplicitimpulsiveproblemundercaputofractionalboundaryconditions
AT fahdjarad mathematicalanalysisofnonlocalimplicitimpulsiveproblemundercaputofractionalboundaryconditions
_version_ 1714998259070533632

Similar Items