A discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b-metric spaces

A discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b-metric spaces

Abstract In this paper, we investigate the existence of positive solutions for the new class of boundary value problems via ψ-Hilfer fractional differential equations. For our purpose, we use the α − ψ $\alpha -\psi $ Geraghty-type contraction in the framework of the b-metric space. We give an examp...

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Main Authors: Hojjat Afshari, Erdal Karapınar
Format: Article
Language:English
Published: SpringerOpen 2020-10-01
Series:Advances in Difference Equations
Subjects:
ψ-Hilfer fractional derivative
Fixed point
Positive solution
Geraghty-type contraction
Online Access:http://link.springer.com/article/10.1186/s13662-020-03076-z
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spelling doaj-ec02c5a147f943bb91cbd350ca79a0652020-11-25T04:06:10ZengSpringerOpenAdvances in Difference Equations1687-18472020-10-012020111110.1186/s13662-020-03076-zA discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b-metric spacesHojjat Afshari0Erdal Karapınar1Department of Mathematics, Faculty of Basic Science, University of BonabDivision of Applied Mathematics, Thu Dau Mot UniversityAbstract In this paper, we investigate the existence of positive solutions for the new class of boundary value problems via ψ-Hilfer fractional differential equations. For our purpose, we use the α − ψ $\alpha -\psi $ Geraghty-type contraction in the framework of the b-metric space. We give an example illustrating the validity of the proved results.http://link.springer.com/article/10.1186/s13662-020-03076-zψ-Hilfer fractional derivativeFixed pointPositive solutionGeraghty-type contraction
collection DOAJ
language English
format Article
sources DOAJ
author Hojjat Afshari
Erdal Karapınar
spellingShingle Hojjat Afshari
Erdal Karapınar
A discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b-metric spaces
Advances in Difference Equations
ψ-Hilfer fractional derivative
Fixed point
Positive solution
Geraghty-type contraction
author_facet Hojjat Afshari
Erdal Karapınar
author_sort Hojjat Afshari
title A discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b-metric spaces
title_short A discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b-metric spaces
title_full A discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b-metric spaces
title_fullStr A discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b-metric spaces
title_full_unstemmed A discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b-metric spaces
title_sort discussion on the existence of positive solutions of the boundary value problems via ψ-hilfer fractional derivative on b-metric spaces
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2020-10-01
description Abstract In this paper, we investigate the existence of positive solutions for the new class of boundary value problems via ψ-Hilfer fractional differential equations. For our purpose, we use the α − ψ $\alpha -\psi $ Geraghty-type contraction in the framework of the b-metric space. We give an example illustrating the validity of the proved results.
topic ψ-Hilfer fractional derivative
Fixed point
Positive solution
Geraghty-type contraction
url http://link.springer.com/article/10.1186/s13662-020-03076-z
work_keys_str_mv AT hojjatafshari adiscussionontheexistenceofpositivesolutionsoftheboundaryvalueproblemsviapshilferfractionalderivativeonbmetricspaces
AT erdalkarapınar adiscussionontheexistenceofpositivesolutionsoftheboundaryvalueproblemsviapshilferfractionalderivativeonbmetricspaces
AT hojjatafshari discussionontheexistenceofpositivesolutionsoftheboundaryvalueproblemsviapshilferfractionalderivativeonbmetricspaces
AT erdalkarapınar discussionontheexistenceofpositivesolutionsoftheboundaryvalueproblemsviapshilferfractionalderivativeonbmetricspaces
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