On almost automorphic solutions of linear operational-differential equations

We prove almost periodicity and almost automorphy of bounded solutions of linear differential equations x′(t)=Ax(t)+f(t) for some class of linear operators acting in a Banach space

Topics in almost automorphy

Presents contributions to the topics of almost periodicity and almost automorphy. Almost periodicity and almost automorphy are also developed on the general structures called fuzzy-number type spaces. This monograph is of interest to researchers and graduate students from many mathematical fields

An Existence Result for Neutral Delay Integrodifferential Equations with Fractional Order and Nonlocal Conditions

We study the existence of mild solutions of a class of neutral delay integrodifferential equations with fractional order and nonlocal conditions in a Banach space X. An existence result on the mild solution is obtained by using the theory of the measures of noncompactness and the theory of condensing maps. Two examples are given to illustrate the existence theorem

On some classes of almost periodic functions in abstract spaces

We deal with C(n)-almost periodic functions taking values in a Banach space. We give several properties of such functions, in particular, we investigate their behavior in view of differentiation as well as integration. The superposition operator acting in the space of such functions is also under consideration. Some applications to ordinary as well as partial differential equations are presented. Moreover, we introduce the class of the so-called asymptotically C(n)-almost periodic functions and give some of their properties

Instantaneous and Noninstantaneous Impulsive Integrodifferential Equations in Banach Spaces

This paper deals with some existence of mild solutions for two classes of impulsive integrodifferential equations in Banach spaces. Our results are based on the fixed point theory and the concept of measure of noncompactness with the help of the resolvent operator. Two illustrative examples are given in the last section