Since the publication of our first book [80], there has been a real resiu-gence of interest in
the study of almost automorphic functions and their applications ([16, 17, 28, 29, 30, 31, 32 …

We introduce the concept of α-resolvent families to prove the existence of almost
automorphic mild solutions to the differential equation Dtαu (t)= Au (t)+ tnf (t), 1≤ α≤ 2, n∈ …

In this paper, we prove that the space (PAA(R,X),‖⋅‖_0) is complete. This not only gives
an affirmative answer to a basic problem in this field, but also enables us to obtain an …

This paper is concerned with weighted pseudo almost automorphic functions, which are
more general and complicated than weighted pseudo almost periodic functions. Using these …

In this paper we are concerned with a (new) class of (Stepanov-like) almost automorphic (Sp-
aa) functions with values in a Banach space X. This class contains the space AA (X) of all …

The concept of square-mean almost automorphy for stochastic processes is introduced. The
existence and uniqueness of square-mean almost automorphic solutions to some linear and …

S-asymptotically ω-periodic solutions of semilinear fractional integro-differential equations -
ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books Search …

We are concerned with the semilinear differential equation in a Banach space $\mathbb {X}
$,\[x'(t)= Ax (t)+ F (t, x (t)),\;\t\in\mathbb {R},\] where $ A $ generates an exponentially stable …

In this paper, we study a new class of functions, which we call (ω, c)‐asymptotically periodic
functions. This collection includes asymptotically periodic, asymptotically antiperiodic …

We study almost automorphic (mild) solutions of the semilinear fractional equation∂ tαu=
Au+∂ tα− 1f (⋅, u), 1< α< 2, considered in a Banach space X, where A is a linear operator of …