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Advanced Topics in Fractional Differential Equations [electronic resource] : A Fixed Point Approach / by Mouffak Benchohra, Erdal Karapinar, Jamal Eddine Lazreg, Abdelkrim Salim.

By: Benchohra, Mouffak [author.].
Contributor(s): Karapinar, Erdal [author.] | Lazreg, Jamal Eddine [author.] | Salim, Abdelkrim [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Synthesis Lectures on Mathematics & Statistics: Publisher: Cham : Springer Nature Switzerland : Imprint: Springer, 2023Edition: 1st ed. 2023.Description: XI, 180 p. 1 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783031269288.Subject(s): Differential equations | Mathematics | Mathematical analysis | Integral equations | Difference equations | Functional equations | Functional analysis | Differential Equations | Mathematics | Analysis | Integral Equations | Difference and Functional Equations | Functional AnalysisAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 515.35 Online resources: Click here to access online
Contents:
Introduction -- Preliminary Background -- Implicit Fractional Differential Equations -- Fractional Differential Equations with Instantaneous Impulses -- Fractional Differential Equations with Non-Instantaneous Impulses.
In: Springer Nature eBookSummary: This book explores fractional differential equations with a fixed point approach. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations. All of the problems in the book also deal with some form of of the well-known Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. Classical and new fixed point theorems, associated with the measure of noncompactness in Banach spaces as well as several generalizations of the Gronwall's lemma, are employed as tools. The book is based on many years of research in this area, and provides suggestions for further study as well. The authors have included illustrations in order to support the readers' understanding of the concepts presented. · Includes illustrations in order to support readers understanding of the presented concepts · Approaches the topic of fractional differential equations while employing fixed point theorems as tools · Presents novel results, which build upon previous literature and many years of research by the authors.
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Introduction -- Preliminary Background -- Implicit Fractional Differential Equations -- Fractional Differential Equations with Instantaneous Impulses -- Fractional Differential Equations with Non-Instantaneous Impulses.

This book explores fractional differential equations with a fixed point approach. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations. All of the problems in the book also deal with some form of of the well-known Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. Classical and new fixed point theorems, associated with the measure of noncompactness in Banach spaces as well as several generalizations of the Gronwall's lemma, are employed as tools. The book is based on many years of research in this area, and provides suggestions for further study as well. The authors have included illustrations in order to support the readers' understanding of the concepts presented. · Includes illustrations in order to support readers understanding of the presented concepts · Approaches the topic of fractional differential equations while employing fixed point theorems as tools · Presents novel results, which build upon previous literature and many years of research by the authors.

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