In this paper we investigate the existence three positives solutions by using Leggett-Williams fixed point theorem in cones for three boundary value problem with fractional order and infinite delay.

In this paper we investigate the existence of at least one, two positive solutions by using the Krasnoselskii fixed-point theorem in cones for nonlinear boundary value problem with fractional order.

In this article, we establish certain sufficient conditions to show the existence of solutions of a fractional differential equation with the ?-Riemann-Liouville and ?-Caputo fractional derivative in a special Banach space. Our approach is based on fixed point theorems for Meir-Keeler condensing operators via measure of non-compactness. Also an example is given to illustrate our approach.

Our aim in this paper is to study the existence and uniqueness of a mild solution to an initial value problem (IVP for short) for a class of nonlinear differential evolution equations with nonlocal initial conditions in a Banach space. We assume that the linear part is not necessarily densely defined and generates an evolution family. We give two results, the first one is based on a Krasnosel'skii fixed point Theorem, and in the second approach we make use Mönch fixed point Theorem combined with the measure of noncompactness and condensing. KeywordsNonlocal initial value problem, evolution family, measure of noncompactness, condensing map, nondensely defined operators, mild solution, Mönch fixed point Theorem.

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