Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities

ISBN-13: 9783319521404 / Angielski / Twarda / 2017 / 414 str.

Bashir Ahmad; Ahmed Alsaedi; Sotiris Ntouyas

Opis

This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral.

Recenzje

"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 Petrusel, 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)

Spis treści

1. Preliminaries.- 2. IVP and BVP for Hadamard-type differential equations and inclusions.- 3. Nonlocal Hadamard fractional boundary value problems.- 4. Fractional integro-differential equations and inclusions.- 5. Fractional differential equations with Hadamard fractional integral conditions.- 6. Hadamard type coupled systems of fractional differential equations.- 7. Nonlinear Langevin equation and inclusions of Hadamard-Caputo type.- 8. Impulsive multi-order Hadamard fractional differential equations.- 9. IVP and BVP for Hybrid Hadamard Fractional Differential Equations and Inclusions.- 10. Positive solutions for Hadamard fractional differential equations on infinite domain.- 11. Fractional integral inequalities via Hadamard's fractional integral.- References.- Index.

O autorze

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. 

Blurb

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.