FRACTIONAL DIFFERENTIAL EQUATIONS AND INCLUSIONS

This monograph is devoted to the existence and stability (Ulam–Hyers–Rassias stability and asymptotic stability) of solutions for various classes of functional differential equations or inclusions involving the Hadamard or Hilfer fractional derivative. Some equations present delay which may be finite, infinite, or state-dependent. Others are subject to impulsive effect which may be fixed or non-instantaneous.

Readers will find the book self-contained and unified in presentation. It provides the necessary background material required to go further into the subject and explores the rich research literature in detail. Each chapter concludes with a section devoted to notes and bibliographical remarks and all abstract results are illustrated by examples. The tools used include many classical and modern nonlinear analysis methods such as fixed-point theorems, as well as some notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. It is useful for researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and all other applied sciences.

Contents:

• Preliminary Background
• Hadamard and Hilfer Fractional Differential Equations and Inclusions in Banach Spaces
• Attractivity Results for Hilfer Fractional Differential Equations
• Ulam Stability Results for Hilfer Fractional Differential Equations
• Random Hilfer Fractional Differential Equations and Inclusions
• Nonlinear Hadamard–Pettis Fractional Integral Equations
• Nonlinear Implicit Hadamard–Pettis Fractional Differential Equations
• Hilfer–Pettis Fractional Differential Equations and Inclusions
• Implicit Hilfer–Pettis Fractional Differential Equations

Readership: Researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and other applied sciences.

Key Features:

• This monograph is devoted to the existence and stability for various classes of functional differential equations or inclusions involving the Hadamard or Hilfer fractional derivative. There are only a few systematic discussions on these contents in published books
• Many new results are presented and this represents the main difference between this book and competitive titles
• A good supplement to the existing literature on fractional differential equations