We study the existence of mild solutions for the two-term fractional order abstract differential equation Dα+1 t u(t)+ μD β t u(t)−Au(t) = D α−1 t f (t,u(t)), t ∈ [0,1], 0 < α ≤ β ≤ 1, μ ≥ 0, with nonlocal initial conditions and where A is a linear operator of sectorial type. To achieve our goal, we use a new mixed method, which combines a generalization of the theory of C0semigroups, Hausdorff...

Abstract. This paper presents new sequence spacesX(r, s, t, p;B) forX ∈ {l∞(p), c(p), c0(p), l(p)} defined by using generalized means and difference operator. It is shown that these spaces are complete paranormed spaces and the spaces X(r, s, t, p;B) for X ∈ {c(p), c0(p), l(p)} have Schauder basis. Furthermore, the α-, β-, γduals of these sequence spaces are computed and also obtained necessary...

We establish the characterisations of classes bounded linear operators from generalised Hahn sequence space hd, where d is an unbounded monotone increasing positive real numbers, into spaces w0, w and w? sequences that are strongly summable to zero, by Ces?ro method order one. Furthermore, we prove estimates for Hausdorff measure noncompactness hd w, identities use these results characterise co...

in this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the fr´echet spaces. our aim is to provide a few generalization of tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of tych...

We prove that the convergence of a sequence of functions in the space L0 of measurable functions, with respect to the topology of convergence in measure, implies the convergence μ-almost everywhere (μ denotes the Lebesgue measure) of the sequence of rearrangements. We obtain nonexpansivity of rearrangement on the space L∞, and also on Orlicz spaces LN with respect to a finitely additive extende...

The present research is concern to the solution of a class mild solutions linked impulsive Hilfer fractional differential equations driven Brownian motion with non-compact semi group in Hilbert spaces. All more obviously Hausdorff measure noncompactness has been utilized get these new results, like manner, arguments were scarred by following tools such as Darbo-Sadovskii fixed point theorem pri...

The purpose of this article is to introduce the notion of cone valued measure of noncompactness. Our theoretical approach generalizes recent results for cone measure of noncompactness. For the proofs of our results we use the famous Schauder-Tichonov Theorem as well as Robert Cauty theorem in the new framework.

This paper is concerned with the existence of mild solutions for impulsive integro-differential equations with nonlocal conditions. We apply the technique measure of noncompactness in the space of piecewise continuous functions and by using Darbo-Sadovskii's fixed point theorem, we prove reasults about impulsive integro-differential equations for convex-power condensing operators.

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.