Abstract The present paper deals with some existence results for the Darboux problem of partial fractional random differential equations finite delay. arguments are based on a fixed point theorem stochastic domain combined measure noncompactness. An illustration is given to show applicability our results.

We extend the classical inverse and implicit function theorems, the implicit function theorems of Lyusternik and Graves, and the results of Clarke and Pourciau to the situation when the given function is not smooth, but it has a convex strict prederivative whose measure of noncompactness is smaller than its measure of surjectivity. The proof of the main results requires Banach’s open mapping th...

In this paper, a new class of abstract impulsive Riemann-Liouville fractional partial neutral functional differential equations with infinite delay is introduced. We apply the suitable fixed point theorem together with the Hausdorff measure of noncompactness to investigate the existence of mild solutions for these equations in Banach spaces. Finally, two examples to illustrate the applications ...

This paper is concerned with the existence of solutions of nonlinear fractional differential inclusions with boundary conditions in a Banach space. The main result is obtained by using the set-valued analog of Mönch fixed point theorem combined with the Kuratowski measure of noncompactness. Mathematics subject classification (2010): 26A33, 34A60, 34B15.

We consider a very general quadratic integral equation and we prove the existence of monotonic solutions of this equation in C[0,1]. Our analysis depends on a suitable combination of the measure of noncompactness introduced by Banaś and Olszowy and the Darabo fixed point theorem.

In this paper we prove theorems on the existence of integrable and monotonic solutions of nonlinear integral equation in Lebesgue Space. The basic tool used in the proof is the fixed point theorem due to Darbo with respect to the so-called measure of weak noncompactness.