<p style='text-indent:20px;'>We discuss the existence and uniqueness of mild solutions for a class quasi-linear fractional integro-differential equations with impulsive conditions via Hausdorff measures noncompactness fixed point theory in Banach space. Mild solution controllability is discussed two particular cases.</p>

This paper is devoted to studying the representation of measures non-generalized compactness, in particular, noncompactness, non-weak compactness and non-super weak etc., defined on Banach spaces its applications. With aid a three-time order-preserving embedding theorem, we show that for every space X, there exist function C(K) some compact Hausdorff K an affine mapping $$\mathbb{T}$$ from supe...

Abstract In this paper, we study the existence and some stability results of mild solutions for random impulsive stochastic integro-differential equations (RISIDEs) with noncompact semigroups in Hilbert spaces via resolvent operators. Initially, prove solution system is established by using Mönch fixed point theorem contemplating Hausdorff measures noncompactness. Then, includes continuous depe...

We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work. 

In this paper, using the concept of measure of noncompactness, which is a very useful and powerful tools in nonlinear functional analysis, metric fixed point theory and integral equations, we introduce a new contraction on a Banach space. For this purpose by using of a measure of noncompactness on a finite product space, we obtain some generalizations of Darbo’s fixed-point theorem. Then, with ...

G. Darbo [Rend. Sem. Math. Univ. Padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.