Motivated by the open question posed H. K. XU in [39] (Question 2:8), Belhadj, Ben Amar and Boumaiza introduced [5] concept of Meir-Keeler condensing operator for self-mappings a Banach space via an arbitrary measure weak noncompactness. In this paper, we introduce Meir- Keeler nonself-mappings noncompactness establish fixed point results under condition Leray-Schauder type. Some basic hybrid t...

In this paper, we deal with the existence of integrable solutions Gripenberg-type equations m-product fractional operators on a half-line R+=[0,∞). We prove in some weighted spaces functions, i.e., so-called L1N-solutions. Because such space is not Banach algebra respect to pointwise product, cannot follow idea proof for continuous solutions, and prefer fixed point approach concerning measure n...

In this paper, we present some alternative results concerning with the existence and attractivity dependence of solutions for a class of nonlinear fractional functional differential equations. In our consideration, we apply the well-known Schauder fixed point theorem in conjunction with the technique of measure of noncompactness. Moreover, we provide examples to illustrate the effectiveness of ...

This paper is concerned with a class of partial nonlocal neutral functional differential and integrodifferential equations with bounded delay in Banach spaces, which are more general than those models been studied. Some existence results of mild solutions to such problems are obtained under the conditions in respect of the Hausdorff’s measure of noncompactness.

In this paper, we extend a monotone iterative technique for nonlocal fractional differential equations with finite delay in an ordered Banach space. By using the monotone iterative technique, theory of fractional calculus, semigroup theory and measure of noncompactness, we study the existence and uniqueness of extremal mild solutions. An example is presented to illustrate the main result.

This paper is concerned with semilinear differential equations with nonlocal conditions in Banach spaces. Using the tools involving the measure of noncompactness and fixed point theory, existence of mild solutions is obtained without the assumption of compactness or equicontinuity on the associated linear semigroup.

This article concerns the existence of solutions to nonlocal fractional differential equations in Banach spaces. By using a type of newly-defined measure of noncompactness, we discuss this problem in general Banach spaces without any compactness assumptions to the operator semigroup. Some existence results are obtained when the nonlocal term is compact and when is Lipschitz continuous.

In this paper we examine nonlinear integrodifferential inclusions defined in a separable Banach space. Using a compactness type hypothesis involving the ball measure of noncompactness, we establish two existence results. One involving convex-valued orientor fields and the other nonconvex valued ones.