In this paper, we investigate the existence and Ulam-Hyers-Rassias stability of solutions for stochastic differential equations with random impulses. Based on Krasnoselskii?s fixed point theorem, perform investigations to system We apply integral inequality Gronwall type study their stability.

An elastic beam equation (EBEq) described by a fourth-order fractional difference is proposed in this work with three-point boundary conditions involving the Riemann–Liouville operator. New sufficient ensuring solutions’ existence and uniqueness of problem are established. The findings obtained employing properties discrete equations, Banach contraction, Brouwer fixed-point theorems. Further, w...

Abstract In this study, an initial-value problem for a nonlinear Volterra functional integro-differential equation on finite interval was considered. The term in the contains multiple time delays. addition to giving some new theorems existence and uniqueness of solutions equation, authors also prove Hyers-Ulam-Rassias stability Hyers-Ulam equation. proofs use several different tools including B...

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...

In this paper, we prove some stability results concerning the generalized quadratic and quartic type functional equation in the context of nonArchimedean fuzzy normed spaces in the spirit of Hyers-Ulam-Rassias. As applications, we establish some results of approximately generalized quadratic and quartic type mapping in non-Archimedean normed spaces. Also, we show that the assumption of the non-...

We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism f from a Banach algebra into a semisimple commutative...

We approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense. More precisely, we establish a fuzzy Hyers–Ulam–Rassias stability of the quadratic functional equation f(x + y) + f(x − y) = 2f(x) + 2f(y). Our result can be regarded as a generalization of the stability phenomenon in the framework of normed spaces. We also prove a generalized version of fuzzy stability o...

and Applied Analysis 3 Moreover, they also investigated the Hyers-Ulam-Rassias stability of 1.3 by using the direct method see 18 . Indeed, they tried to approximate the even and odd parts of each solution of a perturbed inequality by the even and odd parts of an “exact” solution of 1.3 , respectively. In Theorems 3.1 and 3.3 of this paper, we will apply the fixed point method and prove the Hye...

We propose a new method, called the textit{the weighted space method}, for the study of the generalized Hyers-Ulam-Rassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.

Mathematical modeling helps us to better understand different natural phenomena. Modeling is most of the times based on consideration appropriate equations (or systems equations). Here, differential are well-known be very useful instruments when building mathematical models - specially because that use derivatives offers several interpretations associated with real life laws. Differential class...