The authors investigate the existence of solutions to a class boundary value problems for fractional q-difference equations in Banach space that involves q-derivative Caputo type and nonlinear integral conditions. Their result is based on Mönch’s fixed point theorem technique measures noncompactness. This approach has proved be an interesting useful studying such problems. Some basic concepts f...

Abstract In this manuscript, we study the existence and uniqueness of solutions for a new neutral hybrid nonlinear differential equation in context fractional generalized operator sense ψ -Caputo. To emphasize novelty pure technique noncompactness measures is applied to system based on notion modulus continuity Darbo’s criterion that covers existing results other works published before. The Ula...

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 ...

In this article, we study the controllability of impulsive functional differential equations with nonlocal conditions. We establish sufficient conditions for controllability, via the measure of noncompactness and Mönch fixed point theorem.

In this paper, we apply the Hausdorff measure of noncompactness to obtain the necessary and sufficient conditions for certain matrix operators on the Fibonacci difference sequence spaces `p(F̂ ) and `∞(F̂ ) to be compact, where 1 ≤ p <∞.

We study the existence and stability of solutions for a class of nonlinear functional evolution inclusions involving accretive operators. Our approach is employing the fixed point theory for multivalued maps and using estimates via the Hausdorff measure of noncompactness.

In this paper, we study the existence of mild solutions for quasilinear integrodifferential equations with nonlocal conditions in Banach spaces. The results are established by using Hausdorff’s measure of noncompactness.

We fill the gap in understanding the relationship between mappings which are condensing w.r.t. the measure of noncompactness defined on the hyperspace and multifunctions condensing in the ordinary sense.

Using the techniques of some new measures of noncompactness we prove in this paper some existence theorems concerning the global attractivity and ultimate positivity of the solutions for a nonlinear functional integral equation. Our investigations are placed in the Banach space of real-valued functions defined, continuous and bounded on unbounded intervals together with the applications of a re...