This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus. ContentsPreliminary Background Nonlinear Implicit Fractional Differential Equations Impulsive Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Impulsive NIFDE Integrable Solutions for Implicit Fractional Differential Equations Partial Hadamard Fractional Integral Equations and Inclusions Stability Results for Partial Hadamard Fractional Integral Equations and Inclusions Hadamard–Stieltjes Fractional Integral Equations Ulam Stabilities for Random Hadamard Fractional Integral Equations
A detailed and mathematically rigorous study of implicit fractional differential and integral equations With a focus on the existence and stability of solutions Of interest to researchers and graduate students working in fractional calculus
S. Abbas, U. Saïda, Algeria; M. Benchohra, U. Sidi Bel-Abbès, Algeria; J. R. Graef, U. Tennessee, USA; J. Henderson, Baylor U., USA.
"The book is interestingly and carefully written and would be a valuable addition to the library of all those interested in the analysis of fractional differential and integral equations and dynamical systems."Bo Zhang in: Mathematical Reviews Clippings May 2019 MR3791511 "The book is concise and includes many examples to illustrate different approaches of existence and stability of solutions of NIFDE [nonlinear implicit fractional differential equations]. It may be recommended for graduate students or for researchers who work on analysis of solutions of fractional dynamical systems." Zentralblatt für Mathematik