In this paper, we consider a coupled system of nonlinear fractional differential equations (FDEs), such that both equations have a particular perturbed terms. Using emph{Leray-Schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.

We investigate the problem of L p-maximal regularity on Ba-nach spaces having a Schauder basis. Our results improve those of a recent paper.

We suggest a Schauder basis in Banach spaces of smooth functions and traces of smooth functions on Cantor-type sets. In the construction, local Taylor expansions of functions are used. c ⃝ 2011 Elsevier Inc. All rights reserved.

In this paper, we consider a class of nonlinear fuzzy integral equations of fractional order. The existence and uniqueness of solutions are established by the generalized Schauder theorem and contraction mapping principle.

We have investigated the existence and uniqueness solutions of the nonlinear fractional differential equation of an arbitrary order with integral boundary condition. The result is an application of the Schauder fixed point theorem and the Banach contraction principle.

The Banach fixed point theorem and a nonlinear alternative of Leray-Schauder type are used to investigate the existence and uniqueness of solutions for fractional order Hadamard-type functional and neutral functional differential equations.

We examine a certain class of Schauder bases for the space C[−1, 1] consisting of algebraic polynomials orthogonal with respect to the Chebycheff weight of the first kind. We give an improved estimate for its Lebesgue constants.

The Schauder estimate for the Laplace equation was traditionally built upon the Newton potential theory. Different proofs were found later by Campanato [Ca], in which he introduced the Campanato space; Peetre [P], who used the convolution of functions; Trudinger [T], who used the mollification of functions; and Simon [Si], who used a blowup argument. Also a perturbation argument was found by Sa...

We prove the unique existence of a classical solution for a linear parabolic system of nondivergence and nondiagonal form. The key ingredient is to combine the energy estimates with Schauder estimates and to obtain a uniform boundedness of a solution.

In this paper, an existence theorem for a nonlinear two point boundary value problem of second order differential equations in Banach algebras is proved using a nonlinear alternative based on Leray-Schauder alternative.