This manuscript presents Hyers-Ulam stability and Hyers--Ulam--Rassias stability results of non-linear Volterra integro--delay dynamic system on time scales with fractional integrable impulses. Picard fixed point theorem  is used for obtaining  existence and uniqueness of solutions. By means of   abstract Gr"{o}nwall lemma, Gr"{o}nwall's inequality on time scales, we establish  Hyers-Ulam stabi...

We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly contractive condition in partially ordered complete $G$-metric spaces. Some examples are furnished to illustrate the useability of our main results. At the end, an application is presented to the study of exi...

In this study, we consider two different inequivalent formulations of the logistic difference equation $x_{n+1}= beta x_n(1- x_n), n=0,1,..., $ where $x_n$ is a sequence of fuzzy numbers and $beta$ is a positive fuzzy number. The major contribution of this paper is to study the existence, uniqueness and global behavior of the solutions for two corresponding equations, using the concept of Huku...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

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.