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This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.

Mathematics. --- Ordinary Differential Equations. --- Dynamical Systems and Ergodic Theory. --- Systems Theory, Control. --- Differentiable dynamical systems. --- Differential Equations. --- Systems theory. --- Mathématiques --- Dynamique différentiable --- Differential inclusions. --- Functional differential equations. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Inclusions, Differential --- Differential equations, Functional --- Dynamics. --- Ergodic theory. --- Differential equations. --- System theory. --- Differentiable dynamical systems --- Differential equations --- Set-valued maps --- Functional equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- 517.91 Differential equations --- Systems, Theory of --- Systems science --- Science --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Philosophy

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During the last decade, there has been an explosion of interest in fractional dynamics as it was found to play a fundamental role in the modeling of a considerable number of phenomena; in particular the modeling of memory-dependent and complex media. Fractional calculus generalizes integrals and derivatives to non-integer orders and has emerged as an important tool for the study of dynamical systems where classical methods reveal strong limitations. This book is addressed to a wide audience of researchers working with fractional dynamics, including mathematicians, engineers, biologists, and physicists. This timely publication may also be suitable for a graduate level seminar for students studying differential equations.   Topics in Fractional Differential Equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. In this book, problems are studied using the fixed point approach, the method of upper and lower solution, and the Kuratowski measure of noncompactness. An historical introduction to fractional calculus will be of general interest to a wide range of researchers. Chapter one contains some preliminary background results. The second Chapter is devoted to fractional order partial functional differential equations. Chapter three is concerned with functional partial differential inclusions, while in the fourth chapter, we consider functional impulsive partial hyperbolic differential equations. Chapter five is concerned with impulsive partial hyperbolic functional differential inclusions. Implicit partial hyperbolic differential equations are considered in Chapter six, and finally in Chapter seven, Riemann-Liouville fractional order integral equations are considered. Each chapter concludes with a section devoted to notes and bibliographical remarks. The work is self-contained but also contains questions and directions for further research.

Differential equations, Partial. --- Fractional calculus. --- Functional equations. --- Mathematics. --- Fractional calculus --- Differential equations --- Differential equations, Partial --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Differential equations, Hyperbolic. --- Functional differential equations. --- Hyperbolic differential equations --- Differential equations, Functional --- Difference equations. --- Integral equations. --- Partial differential equations. --- Partial Differential Equations. --- Integral Equations. --- Difference and Functional Equations. --- Functional equations --- Differential equations, partial. --- Equations, Functional --- Functional analysis --- Equations, Integral --- Partial differential equations --- Calculus of differences --- Differences, Calculus of --- Equations, Difference

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Algebra --- Partial differential equations --- Mathematics --- differentiaalvergelijkingen --- algebra --- wiskunde

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