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Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities

  • Book
  • © 2017

Overview

Authors:
  1. Bashir Ahmad

    1. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

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  2. Ahmed Alsaedi

    1. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

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  3. Sotiris K. Ntouyas

    1. Department of Mathematics, University of Ioannina, Ioannina, Greece

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  4. Jessada Tariboon

    1. Department of Mathematics, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand

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  • Provides a comprehensive study of recent developments involving Hadamard derivative and integral

  • Offers new research from the authors on initial and boundary value problems in relation to Hadamard-type differential equations and inclusions

  • Perfect for the experienced reader interested in new research and development in the field of fractional differential equations

  • Includes supplementary material: sn.pub/extras

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Preliminaries

    • Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas, Jessada Tariboon
    Pages 1-11

  3. Initial and Boundary Value Problems of Fractional Order Hadamard-Type Functional Differential Equations and Inclusions

    • Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas, Jessada Tariboon
    Pages 13-43

  4. Nonlocal Hadamard Fractional Boundary Value Problems

    • Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas, Jessada Tariboon
    Pages 45-86

  5. Existence Results for Mixed Hadamard and Riemann-Liouville Fractional Integro-Differential Equations and Inclusions

    • Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas, Jessada Tariboon
    Pages 87-108

  6. Nonlocal Hadamard Fractional Integral Conditions and Nonlinear Riemann-Liouville Fractional Differential Equations and Inclusions

    • Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas, Jessada Tariboon
    Pages 109-172

  7. Coupled Systems of Hadamard and Riemann-Liouville Fractional Differential Equations with Hadamard Type Integral Boundary Conditions

    • Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas, Jessada Tariboon
    Pages 173-208

  8. Nonlinear Langevin Equation and Inclusions Involving Hadamard-Caputo Type Fractional Derivatives

    • Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas, Jessada Tariboon
    Pages 209-261

  9. Boundary Value Problems for Impulsive Multi-Order Hadamard Fractional Differential Equations

    • Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas, Jessada Tariboon
    Pages 263-295

  10. Initial and Boundary Value Problems for Hybrid Hadamard Fractional Differential Equations and Inclusions

    • Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas, Jessada Tariboon
    Pages 297-330

  11. Positive Solutions for Hadamard Fractional Differential Equations on Infinite Domain

    • Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas, Jessada Tariboon
    Pages 331-346

  12. Fractional Integral Inequalities via Hadamard’s Fractional Integral

    • Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas, Jessada Tariboon
    Pages 347-401

  13. Back Matter

    Pages 403-414
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Keywords

About this book

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.

Reviews

“The book offers a comprehensive study of the above-mentioned problems, based, in a consistent manner, on the recent studies of the authors, as well as on some relevant results in fractional calculus literature of the last decade. … a nice documented study, very useful for graduate and post-graduate students and for researchers interested in nonlinear applied analysis in general, and fractional analysis in particular.” (Adrian Petruşel, Mathematical Reviews, November, 2017)



“In this nicely written monograph, the authors present a comprehensive treatment of the application of the Hadamard-type fractional derivative to both fractional differential equations and fractional differential inclusions. … this book is very well written and is enjoyable to read. For researchers who have a basic grasp of the fundamentals of the fractional calculus, this book will provide a wealth of ideas for research projects and, more generally, hours of interesting and worthwhile reading.” (Christopher Goodrich, zbMATH 1370.34002, 2017)

Authors and Affiliations

  • Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

    Bashir Ahmad, Ahmed Alsaedi

  • Department of Mathematics, University of Ioannina, Ioannina, Greece

    Sotiris K. Ntouyas

  • Department of Mathematics, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand

    Jessada Tariboon

About the authors

Bashir Ahmad is a professor in the Department of Mathematics at King Abdulaziz University, and in 2009 he was awarded Best Researcher of King Abdulaziz University. His field of research is differential equations and applications, specifically in topics such as set-valued differential equations, functional differential equations, stability analysis, and fluid mechanics.

Ahmed Alsaedi is an associate professor and the chairman of the Department of Mathematics at King Abdulaziz University. 


Sotiris K. Ntouyas is professor emeritus in the Department of Mathematics at the University of Ioannina. He's published numerous books and articles throughout his career, including "Existence results for fractional order functional differential equations with infinite delay," which was awarded the "Top Cited Article 2005-2010" by the Journal of Mathematical Analysis & Applications. 


Jessada Tariboon is a professor in the Department of Mathematics at King Mongkut's University of Technology. He is an editor for King Mongkut's Universty of Technology's International Journal of Applied Science and Technology. 

Bibliographic Information

  • Book Title: Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities

  • Authors: Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas, Jessada Tariboon

  • DOI: https://doi.org/10.1007/978-3-319-52141-1

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Hardcover ISBN: 978-3-319-52140-4Published: 23 March 2017

  • Softcover ISBN: 978-3-319-84831-0Published: 04 May 2018

  • eBook ISBN: 978-3-319-52141-1Published: 16 March 2017

  • Edition Number: 1

  • Number of Pages: XIII, 414

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Analysis, Numerical Analysis

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