This monograph aims to provide for the first time a unified and homogenous presentation of the recent works on the theory of Bloch periodic functions, their generalizations, and their applications to evolution equations. It is useful for graduate students and beginning researchers as seminar topics, graduate courses and reference text in pure and applied mathematics, physics, and engineering.

This book presents and discusses new developments in the study of evolutionary processes. Topics discussed include evolution of magneto-acoustic waves in isothermal atmosphere, quantum dynamical semigroups, traveling waves in discrete models of biological population, motion of electrorheological fluids, Stacklberg control of a backward linear heat equation, Leray weak solutions of Navier-Stokes equation involving one directional derivative, and initial value boundary problem of an evolutionary p(x)-Laplacian equation.

This volume of Advances in Evolution Equations is dedicated to the memory of Professor Vasilii Vasilievich Zhikov, an outstanding Russian mathematician. Zhikov's scientific interest ranged from almost periodic differential equations and topological dynamics to spectral theory of elliptic operators, qualitative theory of parabolic equations, calculus of variations, homogenization, and hydrodynamics, to name a few. Many of his results are now classical.

Fractional calculus deals with extensions of derivatives and integrals to non-integer orders. It represents a powerful tool in applied mathematics to study a myriad of problems from different fields of science and engineering, with many break-through results found in mathematical physics, finance, hydrology, biophysics, thermodynamics, control theory, statistical mechanics, astrophysics, cosmology and bioengineering. This book is devoted to the existence and uniqueness of solutions and some Ulam's type stability concepts for various classes of functional differential and integral equations of fractional order. Some equations present delay which may be finite, infinite or state-dependent. Others are subject to multiple time delay effect. The tools used include classical fixed point theorems. Other tools are based on the measure of non-compactness together with appropriates fixed point theorems. Each chapter concludes with a section devoted to notes and bibliographical remarks and all the presented results are illustrated by examples. The content of the book is new and complements the existing literature in Fractional Calculus. It is useful for researchers and graduate students for research, seminars and advanced graduate courses, in pure and applied mathematics, engineering, biology and other applied sciences.