On a class of boundary value problems under ABC fractional derivative

On a class of boundary value problems under ABC fractional derivative

Abstract In this work, we establish some necessary results about existence theory to a class of boundary value problems (BVPs) of hybrid fractional differential equations (HFDEs) in the frame of Atangana–Baleanu–Caputo (ABC) fractional derivative. Making use of Krasnoselskii and Banach theorems, we...

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Main Authors: Rozi Gul, Kamal Shah, Zareen A. Khan, Fahd Jarad
Format: Article
Language:English
Published: SpringerOpen 2021-10-01
Series:Advances in Difference Equations
Subjects:
ABC fractional order derivative
HFDEs
Krasnoselskii and Banach theorems
Stability
Online Access:https://doi.org/10.1186/s13662-021-03595-3
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spelling doaj-0d4e6a0069824c358e9c4d89ae2c0c552021-10-03T11:12:39ZengSpringerOpenAdvances in Difference Equations1687-18472021-10-012021111210.1186/s13662-021-03595-3On a class of boundary value problems under ABC fractional derivativeRozi Gul0Kamal Shah1Zareen A. Khan2Fahd Jarad3Department of Mathematics, University of MalakandDepartment of Mathematics, University of MalakandDepartment of Mathematical Sciences, Faculty of Science, Princess Nourah bint Abdulrahman UniversityDepartment of Mathematics, Cankaya UniversityAbstract In this work, we establish some necessary results about existence theory to a class of boundary value problems (BVPs) of hybrid fractional differential equations (HFDEs) in the frame of Atangana–Baleanu–Caputo (ABC) fractional derivative. Making use of Krasnoselskii and Banach theorems, we obtain the required conditions. Some appropriate results of Hyers–Ulam (H–U) stability corresponding to the considered problem are also established. Also a pertinent example is given to demonstrate the results.https://doi.org/10.1186/s13662-021-03595-3ABC fractional order derivativeHFDEsKrasnoselskii and Banach theoremsStability
collection DOAJ
language English
format Article
sources DOAJ
author Rozi Gul
Kamal Shah
Zareen A. Khan
Fahd Jarad
spellingShingle Rozi Gul
Kamal Shah
Zareen A. Khan
Fahd Jarad
On a class of boundary value problems under ABC fractional derivative
Advances in Difference Equations
ABC fractional order derivative
HFDEs
Krasnoselskii and Banach theorems
Stability
author_facet Rozi Gul
Kamal Shah
Zareen A. Khan
Fahd Jarad
author_sort Rozi Gul
title On a class of boundary value problems under ABC fractional derivative
title_short On a class of boundary value problems under ABC fractional derivative
title_full On a class of boundary value problems under ABC fractional derivative
title_fullStr On a class of boundary value problems under ABC fractional derivative
title_full_unstemmed On a class of boundary value problems under ABC fractional derivative
title_sort on a class of boundary value problems under abc fractional derivative
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2021-10-01
description Abstract In this work, we establish some necessary results about existence theory to a class of boundary value problems (BVPs) of hybrid fractional differential equations (HFDEs) in the frame of Atangana–Baleanu–Caputo (ABC) fractional derivative. Making use of Krasnoselskii and Banach theorems, we obtain the required conditions. Some appropriate results of Hyers–Ulam (H–U) stability corresponding to the considered problem are also established. Also a pertinent example is given to demonstrate the results.
topic ABC fractional order derivative
HFDEs
Krasnoselskii and Banach theorems
Stability
url https://doi.org/10.1186/s13662-021-03595-3
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AT zareenakhan onaclassofboundaryvalueproblemsunderabcfractionalderivative
AT fahdjarad onaclassofboundaryvalueproblemsunderabcfractionalderivative
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