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.

Auteur
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 theDepartment 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.

Résumé
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.

Contenu

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.