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Article

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

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Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel Abbes 22000, Algeria
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Department of Mathematics, University of Tennessee, Chattanooga, TN 37403, USA
*
Author to whom correspondence should be addressed.
Received: 10 November 2020 / Revised: 7 December 2020 / Accepted: 16 December 2020 / Published: 22 December 2020
(This article belongs to the Special Issue 2020 Selected Papers from Fractal Fract’s Editorial Board Members)
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. View Full-Text
Keywords: generalized hilfer fractional derivative; implicit fractional differential equations; non-instantaneous impulses; existence; gronwall lemma; fixed point; impulses; ulam stability generalized hilfer fractional derivative; implicit fractional differential equations; non-instantaneous impulses; existence; gronwall lemma; fixed point; impulses; ulam stability
MDPI and ACS Style

Salim, A.; Benchohra, M.; Graef, J.R.; Lazreg, J.E. Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses. Fractal Fract. 2021, 5, 1. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract5010001

AMA Style

Salim A, Benchohra M, Graef JR, Lazreg JE. Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses. Fractal and Fractional. 2021; 5(1):1. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract5010001

Chicago/Turabian Style

Salim, Abdelkrim, Mouffak Benchohra, John R. Graef, and Jamal E. Lazreg 2021. "Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses" Fractal and Fractional 5, no. 1: 1. https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract5010001

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