$Applications of new contraction mappings on existence and uniqueness results for implicit ϕ-Hilfer fractional pantograph differential equations$
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Applications of new contraction mappings on existence and uniqueness results for implicit ϕ-Hilfer fractional pantograph differential equations

Abstract In this paper, we consider initial value problems for two different classes of implicit ϕ-Hilfer fractional pantograph differential equations. We use different approach that is based on α − ψ $\alpha -\psi $ -contraction mappings to demonstrate the existence and uniqueness of solutions for...

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Autores principales:	Hojjat Afshari, H. R. Marasi, Jehad Alzabut
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	α − ψ $\alpha -\psi $ -Contraction mapping ϕ-Hilfer fractional derivative Fractional differential equation Pantograph differential equation Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/ebc9aad3852f4596abb545f36831bd3a
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spelling	oai:doaj.org-article:ebc9aad3852f4596abb545f36831bd3a2021-11-21T12:28:45ZApplications of new contraction mappings on existence and uniqueness results for implicit ϕ-Hilfer fractional pantograph differential equations10.1186/s13660-021-02711-x1029-242Xhttps://doaj.org/article/ebc9aad3852f4596abb545f36831bd3a2021-11-01T00:00:00Zhttps://doi.org/10.1186/s13660-021-02711-xhttps://doaj.org/toc/1029-242XAbstract In this paper, we consider initial value problems for two different classes of implicit ϕ-Hilfer fractional pantograph differential equations. We use different approach that is based on α − ψ $\alpha -\psi $ -contraction mappings to demonstrate the existence and uniqueness of solutions for the proposed problems. The mappings are defined in appropriate cones of positive functions. The presented examples demonstrate the efficiency of the used method and the consistency of the proposed results.Hojjat AfshariH. R. MarasiJehad AlzabutSpringerOpenarticleα − ψ $\alpha -\psi $ -Contraction mappingϕ-Hilfer fractional derivativeFractional differential equationPantograph differential equationMathematicsQA1-939ENJournal of Inequalities and Applications, Vol 2021, Iss 1, Pp 1-14 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	α − ψ $\alpha -\psi $ -Contraction mapping ϕ-Hilfer fractional derivative Fractional differential equation Pantograph differential equation Mathematics QA1-939
spellingShingle	α − ψ $\alpha -\psi $ -Contraction mapping ϕ-Hilfer fractional derivative Fractional differential equation Pantograph differential equation Mathematics QA1-939 Hojjat Afshari H. R. Marasi Jehad Alzabut Applications of new contraction mappings on existence and uniqueness results for implicit ϕ-Hilfer fractional pantograph differential equations
description	Abstract In this paper, we consider initial value problems for two different classes of implicit ϕ-Hilfer fractional pantograph differential equations. We use different approach that is based on α − ψ $\alpha -\psi $ -contraction mappings to demonstrate the existence and uniqueness of solutions for the proposed problems. The mappings are defined in appropriate cones of positive functions. The presented examples demonstrate the efficiency of the used method and the consistency of the proposed results.
format	article
author	Hojjat Afshari H. R. Marasi Jehad Alzabut
author_facet	Hojjat Afshari H. R. Marasi Jehad Alzabut
author_sort	Hojjat Afshari
title	Applications of new contraction mappings on existence and uniqueness results for implicit ϕ-Hilfer fractional pantograph differential equations
title_short	Applications of new contraction mappings on existence and uniqueness results for implicit ϕ-Hilfer fractional pantograph differential equations
title_full	Applications of new contraction mappings on existence and uniqueness results for implicit ϕ-Hilfer fractional pantograph differential equations
title_fullStr	Applications of new contraction mappings on existence and uniqueness results for implicit ϕ-Hilfer fractional pantograph differential equations
title_full_unstemmed	Applications of new contraction mappings on existence and uniqueness results for implicit ϕ-Hilfer fractional pantograph differential equations
title_sort	applications of new contraction mappings on existence and uniqueness results for implicit ϕ-hilfer fractional pantograph differential equations
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/ebc9aad3852f4596abb545f36831bd3a
work_keys_str_mv	AT hojjatafshari applicationsofnewcontractionmappingsonexistenceanduniquenessresultsforimplicitphhilferfractionalpantographdifferentialequations AT hrmarasi applicationsofnewcontractionmappingsonexistenceanduniquenessresultsforimplicitphhilferfractionalpantographdifferentialequations AT jehadalzabut applicationsofnewcontractionmappingsonexistenceanduniquenessresultsforimplicitphhilferfractionalpantographdifferentialequations
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Applications of new contraction mappings on existence and uniqueness results for implicit ϕ-Hilfer fractional pantograph differential equations

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