Hadamard-type fractional differential equations, inclusions and inequalities /

Hadamard-type fractional differential equations, inclusions and inequalities /

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Bibliographic Details
Imprint:Cham, Switzerland : Springer, 2017.
Description:1 online resource (xiii, 414 pages) : illustrations
Language:English
Subject:
Fractional differential equations.
Fractional differential equations.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11272503
Hidden Bibliographic Details
Other authors / contributors:Ahmad, Bashir (Mathematics professor), author.
Alsaedi, Ahmed, author.
Ntouyas, Sotiris, 1950- author.
Tariboon, Jessada, 1975- author.
ISBN:9783319521411
3319521411
9783319521404
3319521403
Digital file characteristics:text file PDF
Notes:Includes bibliographical references and index.
Online resource; title from PDF title page (SpringerLink, viewed March 29, 2017).
Summary:This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential equations and inclusions as well as their functional counterparts. The book covers fundamental concepts of multivalued analysis and introduces a new class of mixed initial value problems involving the Hadamard derivative and Riemann-Liouville fractional integrals. In later chapters, the authors discuss nonlinear Langevin equations as well as coupled systems of Langevin equations with fractional integral conditions. Focused and thorough, this book is a useful resource for readers and researchers interested in the area of fractional calculus.
Other form:Print version: Hadamard-type fractional differential equations, inclusions and inequalities. Cham, Switzerland : Springer, 2017 9783319521404 3319521403
Standard no.:10.1007/978-3-319-52141-1
Table of Contents:
  • Preface; Contents; 1 Preliminaries; 1.1 Definitions and Results from Multivalued Analysis; 1.2 Definitions and Results from Fractional Calculus; 1.3 Fixed Point Theorems; 2 IVP and BVP for Hadamard-Type Differential Equations and Inclusions; 2.1 Introduction; 2.2 Functional and Neutral Fractional Differential Equations; 2.2.1 Functional Differential Equations; 2.2.2 Neutral Functional Differential Equations; 2.2.3 An Example; 2.3 Functional and Neutral Fractional Differential Inclusions; 2.3.1 Functional Differential Inclusions; 2.3.2 Neutral Functional Differential Inclusions.
  • 2.3.3 Examples2.4 BVP for Fractional Order Hadamard-type Functional Differential Equations and inclusions; 2.4.1 Fractional Order Hadamard-Type Functional Differential Equations; 2.4.2 Fractional Order Hadamard-Type Functional Differential Inclusions; 2.5 Notes and Remarks; 3 Nonlocal Hadamard Fractional Boundary Value Problems; 3.1 Introduction; 3.2 A Three-Point Hadamard-Type Fractional Boundary Value Problem; 3.2.1 The Case of Fractional Integral Boundary Conditions; 3.3 Nonlocal Hadamard BVP of Fractional Integro-Differential Equations.
  • 3.3.1 Existence and Uniqueness Result via Banach's Fixed Point Theorem3.3.2 Existence Result via Krasnoselskii's Fixed Point Theorem; 3.3.3 Existence Result via Leray-Schauder's Nonlinear Alternative; 3.3.4 Existence Result via Leray-Schauder's Degree; 3.3.5 A Companion Problem; 3.4 Nonlocal Hadamard BVP of Fractional Integro-Differential Inclusions; 3.4.1 The Carathéodory Case; 3.4.2 The Lower Semicontinuous Case; 3.4.3 The Lipschitz Case; 3.5 Nonlocal Hadamard Fractional Boundary Value Problems; 3.6 Existence Results: The Single-Valued Case; 3.7 Existence Result: The Multivalued Case.
  • 3.8 Notes and Remarks4 Fractional Integro-Differential Equations and Inclusions; 4.1 Introduction; 4.2 Mixed Hadamard and Riemann-Liouville Fractional Integro-Differential Equations; 4.3 Mixed Hadamard and Riemann-Liouville Fractional Integro-Differential Inclusions; 4.3.1 The Upper Semicontinuous Case; 4.3.2 The Lipschitz Case; 4.3.3 Examples; 4.4 Existence Result via Endpoint Theory; 4.5 Notes and Remarks; 5 Factional Differential Equations with Hadamard Fractional Integral Conditions; 5.1 Introduction; 5.2 Nonlocal Hadamard Fractional Differential Equations.
  • 5.2.1 Existence and Uniqueness Result via Banach's Fixed Point Theorem5.2.2 Existence and Uniqueness Result via Banach's Fixed Point Theorem and Hölder's Inequality; 5.2.3 Existence and Uniqueness Result via Nonlinear Contractions; 5.2.4 Existence Result via Krasnoselskii's Fixed Point Theorem; 5.2.5 Existence Result via Leray-Schauder's Nonlinear Alternative; 5.2.6 Existence Result via Leray-Schauder's Degree Theory; 5.3 Nonlocal Hadamard Fractional Differential Inclusions; 5.3.1 The Lipschitz Case; 5.3.2 The Carathéodory Case; 5.3.3 The Lower Semicontinuous Case.

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