The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...

In this paper using the well-known Schauder fixed point theorem we study and obtain the existence of almost periodic mild solutions to some classes of nonautonomous third-order differential equations on a separable infinite dimensional complex Hilbert space.

In this paper, by employing fixed point index theory and Leray-Schauder degree theory, we obtain the existence and multiplicity of sign-changing solutions for nonlinear second-order differential equations with integral boundary value conditions.

Here is established the global existence of smooth solutions to a generalized nonlinear equation of Schrödinger type in the usual Sobolev spaces H and certain weighted Sobolev spaces by using Leray-Schauder fixed point theorem and delicate a priori estimates.

The Banach fixed point theorem and the nonlinear alternative of Leray–Schauder type are used to investigate the existence of solutions for fractional order functional and neutral functional differential equations with infinite delay. © 2007 Elsevier Inc. All rights reserved.

Sufficient conditions for controllability of neutral functional integrodifferential systems in Banach spaces with initial condition in the phase space are established. The results are obtained by using the Schauder fixed point theorem. An example is provided to illustrate the theory.

This paper is concerned with the existence and uniqueness of mild solution to functional fractional fuzzy impulsive differential equations. For the existence and uniqueness we use the Banach fixed point theorem and the nonlinear alternative of Leray-Schauder type.

Motivated by Vityuk and Golushkov (2004), using the Schauder Fixed Point Theorem and the Contraction Principle, we consider existence and uniqueness of positive solution of a singular partial fractional differential equation in a Banach space concerning with fractional derivative.

Conjecture [Schauder] For every non-empty convex subset C of a topological vector space E, a compact continuous mapping f : C → C has a fixed point, i.e., a point x∗ ∈ C such that f(x∗) = x∗. (See [16], problem 54). We recall that a mapping f : C → C is said to be compact if f(C) is contained in a compact subset of C. Schauder proved in 1930 that his conjecture holds for normed vector spaces an...

In this paper, we present a novel idea of unification of anti-periodic and multi-point boundary conditions and develop the existence theory for sequential fractional differential equations supplemented with these new conditions. We apply fixed point theorems due to Banach, Krasnoselskii, Leray-Schauder alternative criterion, and Leray-Schauder degree theory to obtain the desired results. Our re...