In the present paper, we introduces the notion of integral type contractive mapping with respect to ordered S-metric space and prove some coupled common fixed point results of integral type contractive mapping in ordered S-metric space. Moreover, we give an example to support our main result.

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.

In this paper we investigate the existence and uniqueness for Volterra-Fredholm type integral equations and extension of this type of integral equations. The result is obtained by using the  coupled fixed point theorems in the framework of Banach space $ X=C([a,b],mathbb{R})$. Finally, we  give an example to illustrate the applications of our results.

in this paper, we consider a coupled system of nonlinear fractional differential equations (fdes), such that bothequations have a particular perturbed terms. using emph{leray-schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.

Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for stochastic ordinary differential equations is relatively mature. In this paper, we present a unified theory of invariant manifolds for infinite dimensional random ...