this paper presents some results concerning the existence of solutions for a functional integral equation of volterra type in two variables, via measure of noncompactness. two examples are included to illustrate the main result.

This manuscript mainly focused on the nonlocal controllability of Hilfer fractional stochastic differential equations via almost sectorial operators. The key ideas study are illustrated by using from calculus, fixed point technique, and measures noncompactness. Then, authors establish new criteria for mild existence solutions derive fundamental characteristics a system. In addition, researchers...

In this paper we introduce a parameter ω∞ in the space of functions L0. The parameter measures the lack of equimeasurability using a sequence of functions which controls the oscillations of every function of a given subset of L0. We estimate the Hausdorff measure of noncompactness in terms of ω∞ and the parameter σ (see [3]) and characterize the totally bounded subsets of L0. A criterion of com...

This paper addresses some existence, attractivity and controllability results for semilinear integrodifferential equations having non-instantaneous impulsions on an infinite interval via resolvent operators in case of neutral state-dependent delay problems. Our criteria were obtained by applying a Darbo’s fixed-point theorem combined with measures noncompactness. The result is illustrated examp...

Abstract In this paper we estimate the Kuratowski and Hausdorff measures of noncompactness bounded subsets spaces vector-valued functions differentiable functions. To end, use a quantitative characteristic modeled on new equicontinuity-type concept classical characteristics related to pointwise relative compactness. We obtain regular in taken into consideration. The established inequalities red...

In the paper, we prove the existence of solutions and Carathéodory’s type solutions of the dynamic Cauchy problem x(t) = f(t, x(t)), t ∈ T, x(0) = x0, where T denotes an unbounded time scale (a nonempty closed subset of R and such that there exists a sequence (xn) in T and xn → ∞) and f is continuous or satisfies Carathéodory’s conditions and some conditions expressed in terms of measures of no...

The aim of this paper is to investigate the existence anti-periodic solutions for a nonlinear coupled system $$\Psi -$$ Caputo fractional differential equations with $$p-$$ Laplacian operator in Banach space. proofs our main results are based on Mönch’s fixed point theorem and some basic tools calculus paired measures noncompactness. As an application, theoretical have been illustrated by provi...

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...