Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses

This manuscript is devoted to proving some results concerning the existence of solutions to a class of boundary value problems for nonlinear implicit fractional differential equations with non-instantaneous impulses and generalized Hilfer fractional derivatives. The results are based on Banach’s con...

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Main Authors:	Abdelkrim Salim, Mouffak Benchohra, John R. Graef, Jamal Eddine Lazreg
Format:	Article
Language:	English
Published:	MDPI AG 2021-12-01
Series:	Fractal and Fractional
Subjects:	generalized hilfer fractional derivative implicit fractional differential equations non-instantaneous impulses existence gronwall lemma fixed point
Online Access:	https://www.mdpi.com/2504-3110/5/1/1

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spelling	doaj-0c8d471ae75747e49ca3779b68e46eeb2021-04-02T18:58:31ZengMDPI AGFractal and Fractional2504-31102021-12-0151110.3390/fractalfract5010001Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous ImpulsesAbdelkrim Salim0Mouffak Benchohra1John R. Graef2Jamal Eddine Lazreg3Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel Abbes 22000, AlgeriaLaboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel Abbes 22000, AlgeriaDepartment of Mathematics, University of Tennessee, Chattanooga, TN 37403, USALaboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel Abbes 22000, AlgeriaThis manuscript is devoted to proving some results concerning the existence of solutions to a class of boundary value problems for nonlinear implicit fractional differential equations with non-instantaneous impulses and generalized Hilfer fractional derivatives. The results are based on Banach’s contraction principle and Krasnosel’skii’s fixed point theorem. To illustrate the results, an example is provided.https://www.mdpi.com/2504-3110/5/1/1generalized hilfer fractional derivativeimplicit fractional differential equationsnon-instantaneous impulsesexistencegronwall lemmafixed point
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Abdelkrim Salim Mouffak Benchohra John R. Graef Jamal Eddine Lazreg
spellingShingle	Abdelkrim Salim Mouffak Benchohra John R. Graef Jamal Eddine Lazreg Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses Fractal and Fractional generalized hilfer fractional derivative implicit fractional differential equations non-instantaneous impulses existence gronwall lemma fixed point
author_facet	Abdelkrim Salim Mouffak Benchohra John R. Graef Jamal Eddine Lazreg
author_sort	Abdelkrim Salim
title	Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses
title_short	Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses
title_full	Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses
title_fullStr	Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses
title_full_unstemmed	Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses
title_sort	boundary value problem for fractional order generalized hilfer-type fractional derivative with non-instantaneous impulses
publisher	MDPI AG
series	Fractal and Fractional
issn	2504-3110
publishDate	2021-12-01
description	This manuscript is devoted to proving some results concerning the existence of solutions to a class of boundary value problems for nonlinear implicit fractional differential equations with non-instantaneous impulses and generalized Hilfer fractional derivatives. The results are based on Banach’s contraction principle and Krasnosel’skii’s fixed point theorem. To illustrate the results, an example is provided.
topic	generalized hilfer fractional derivative implicit fractional differential equations non-instantaneous impulses existence gronwall lemma fixed point
url	https://www.mdpi.com/2504-3110/5/1/1
work_keys_str_mv	AT abdelkrimsalim boundaryvalueproblemforfractionalordergeneralizedhilfertypefractionalderivativewithnoninstantaneousimpulses AT mouffakbenchohra boundaryvalueproblemforfractionalordergeneralizedhilfertypefractionalderivativewithnoninstantaneousimpulses AT johnrgraef boundaryvalueproblemforfractionalordergeneralizedhilfertypefractionalderivativewithnoninstantaneousimpulses AT jamaleddinelazreg boundaryvalueproblemforfractionalordergeneralizedhilfertypefractionalderivativewithnoninstantaneousimpulses
_version_	1721550198963961856

Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses

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