Correspondence: fangli860@gmail. com School of Mathematics, Yunnan Normal University, Kunming 650092, People’s Republic of China Abstract This article concerns the existence of mild solutions for the fractional integrodifferential equations of neutral type with finite delay and nonlocal conditions in a Banach space X. The existence of mild solutions is proved by means of measure of noncompactne...

We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be det...

An integrodifferential equation with fractional derivatives in the nonlinearities is studied in this article, and some sufficient conditions for existence and uniqueness of a solution for the equation are established by contraction mapping principle.

We derive the single integrodifferential wave equation for the probability density function of the position of a classical one-dimensional Lévy walk with continuous sample paths. This equation involves a classical wave operator together with memory integrals describing the spatiotemporal coupling of the Lévy walk. It is valid at all times, not only in the long time limit, and it does not involv...

Controllability of nonlinear systems represented by ordinary differential equations in infinite-dimensional spaces has been extensively studied by several authors. Naito [12,13] has studied the controllability of semilinear systems whereas Yamamoto and Park [19] discussed the same problem for parabolic equation with uniformly bounded nonlinear term. Chukwu and Lenhart [3] have studied the contr...

This paper is concerned with a nonlocal Cauchy problem for fractional integrodifferential equations in a separable Banach space X. We establish an existence theorem for mild solutions to the nonlocal Cauchy problem, by virtue of measure of noncompactness and the fixed point theorem for condensing maps. As an application, the existence of the mild solution to a nonlocal Cauchy problem for a conc...

In this paper, the existence of mild solutions for the fractional differential equations of neutral type with infinite delay is obtained under the conditions in respect of the Kuratowski’s measure of noncompactness. As an application, the existence of mild solution for some integrodifferential equation is obtained. keywords: fractional differential equation, neutral differential equation, mild ...