In this article, we study the asymptotical stability in p-th moment of mild solutions to a class of fractional impulsive partial neutral stochastic integro-differential equations with state-dependent delay in Hilbert spaces. We assume that the linear part of this equation generates an α-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence and as...

In this paper, we present a novel idea of unification of anti-periodic and multi-point boundary conditions and develop the existence theory for sequential fractional differential equations supplemented with these new conditions. We apply fixed point theorems due to Banach, Krasnoselskii, Leray-Schauder alternative criterion, and Leray-Schauder degree theory to obtain the desired results. Our re...

1 Department of Mathematical Sciences, Florida Institute of Technology, 150 West University Boulevard, Melbourne, FL 32901, USA 2 Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia 3 Department of Mathematics, National University of Ireland, Galway, Ireland 4 Laboratoire de Mathématiques et de Dynamique de Populations, Université C...

In the present paper we establish a fixed point result of Krasnoselskii type for the sum A+B, where A and B are sequentially weakly continuous, and B is a nonexpansive mapping. As an application, we study the existence of solutions for an nonlinear integral equation in Banach spaces. In the last section we develop a sequentially weak continuity result for a class of operators acting on vector-v...

In this paper, some basic hybrid fixed point theorems of Banach and Schauder type and some hybrid fixed point theorems of Krasnoselskii type involving the sum of two operators are proved in a partially ordered normed linear spaces which are further applied to nonlinear Volterra fractional integral equations for proving the existence of solutions under certain monotonic conditions blending with ...

Preisach model has been used extensively since the model has been initially developed by Ferenc Preisach about 75 years ago, especially for ferromagnetic materials. When the model has been analyzed from a mathematical point of view by Krasnoselskii and Pokrovskii and after them by Mayergoys and other scientists it was stated that, in fact, the model is “the best hysteresis model at our disposal...

A set of np ≥2 -cyclic and either continuous or contractive self-mappings, with at least one of them being contractive, which are defined on a set of subsets of a Banach space, are considered to build a composed self-mapping of interest. The existence and uniqueness of fixed points and the existence of best proximity points, in the case that the subsets do not intersect, of such composed mappin...

We study the existence of periodic solutions of the second order nonlinear neutral differential equation with variable delay x′′ (t) + p (t)x′ (t) + q (t)h (x (t)) = c (t)x′ (t− τ (t)) + f (t, x (t− τ (t))) . We invert the given equation to obtain an integral, but equivalent, equation from which we define a fixed point mapping written as a sum of a large contraction and a compact map. We show t...

Since monotone methods have been initiated by Kamke 1 and Müler 2 , and developed further by Krasnoselskii 3, 4 , Matano 5 , and Smith 6 , the theory and application of monotone dynamics have become increasingly important see 7–18 . It is well known that the quasimonotone condition is very important in studying the asymptotic behaviors of dynamical systems. If this condition is satisfied, the s...