In this paper, we consider a Hammerstein integral equation (Hammerstein IE) in two variables with of time delays. The aim paper is to investigate the Hyers–Ulam (HU) stability and Hyers–Ulam–Rassias (HUR) considered IE via Banach’s fixed point theorem (Banach’s FPT) Bielecki metric. proofs new outcomes are based on these basic tools. As contributions present study, here, for first time, develop...

A theorem on asymptotic stability is obtained for a differential equation with an infinite delay in a function space which is suitable for the numerical computation of the solution to the infinite delay equation.

A n umerical method for obtaining a crystalline ow starting from a general polygon is presented. A crystalline ow is a polygonal ow and can be regarded as a discrete version of a classical curvature ow. In some cases, new facets may be created instantaneously and their facet lengths are governed by a system of singular ordinary dierential equations (ODEs). The proposed method solves the system ...

Pairings permit several protocol simplications and original scheme creation, for example Identity Based Cryptography protocols. Initially, the use of pairings did not involve any secret entry, consequently, side channel attacks were not a threat for pairing based cryptography. On the contrary, in an Identity Based Cryptographic protocol, one of the two entries to the pairing is secret. Side Cha...

In this paper, the existence of mild solutions for the fractional differential equations of neutral type with infinite delay is obtained under the conditions in respect of the Kuratowski’s measure of noncompactness. As an application, the existence of mild solution for some integrodifferential equation is obtained. keywords: fractional differential equation, neutral differential equation, mild ...

In this paper, we present a numerical integration method to solve singularly perturbed delay differential equations. In this method, we first convert the second order singularly perturbed delay differential equation to first order neutral type delay differential equation and employ the numerical integration. Then, linear interpolation is used to get three term recurrence relation which is solve...

x0 h and S Cobordism Theorems-review-In this article the author would like to propose a natural generalization of celebrated h and S coboridism theorems to loop space. We will explain some part of the idea of the proof of an (easier) half of it, and also a nite dimensional analogue of the conjecture which can be proved under some additional assumptions. The detailed proof of them will appear el...