In 1940, Ulam proposed the general Ulam stability problem see 1 . Let G1 be a group and let G2 be a metric group with the metric d ·, · . Given ε > 0, does there exist a δ > 0 such that if a mapping h : G1 → G2 satisfies the inequality d h xy , h x h y < δ for all x, y ∈ G1 then there is a homomorphism H : G1 → G2 with d h x ,H x < ε for all x ∈ G1? In 1941, this problem was solved by Hyers 2 i...

the stability problem of the functional equation was conjectured by ulam and was solved by hyers in the case of additive mapping. baker et al. investigated the superstability of the functional equation from a vector space to real numbers.in this paper, we exhibit the superstability of $m$-additive maps on complete non--archimedean spaces via a fixed point method raised by diaz and margolis.

Keywords---Hyers-Ulam-Rassias stability, Functional equation, Riemann zeta function, Square root spital. 1. I N T R O D U C T I O N The staxting point of studying the stability of functional equations seems to be the famous talk of Ulam [2] in 1940, in which he discussed a number of important unsolved problems. Among those was the question concerning the stability of group homomorphisms. Let G1...

This article deals with a class of nonlinear fractional differential equations, initial conditions, involving the Riemann–Liouville derivative order α∈(1,2). The main objectives are to obtain conditions for existence and uniqueness solutions (within appropriate spaces), analyze stabilities Ulam–Hyers Ulam–Hyers–Rassias types. In fact, different obtained based on analysis an associated integral ...

Fractional derivatives are used to model the transmission of many real world problems like COVID-19. It is always hard find analytical solutions for such models. Thus, approximate interest in interesting applications. Stability theory introduces using some conditions. This article devoted investigation stability nonlinear differential equations with Riemann-Liouville fractional derivative. We e...

In this paper, we investigate the Hyers-Ulam stability of the orthogonally  cubic equation and  Pexiderized cubic equation [f(kx+y)+f(kx-y)=g(x+y)+g(x-y)+frac{2}{k}g(kx)-2g(x),]in multi-normed spaces by the direct method and the fixed point method. Moreover, we prove the Hyers-Ulam stability of the  $2$-variables cubic  equation [ f(2x+y,2z+t)+f(2x-y,2z-t) =2...

Abstract In this paper, a class of nonlinear ? -Hilfer fractional integrodifferential coupled systems on bounded domain is investigated. The existence and uniqueness results for the are proved based contraction mapping principle. Moreover, Ulam–Hyers–Rassias, Ulam–Hyers, semi-Ulam–Hyers–Rassias stabilities to initial value problem obtained.

The fractional Langevin equation has more advantages than its classical in representing the random motion of Brownian particles complex viscoelastic fluid. Mittag–Leffler (ML) without singularity is accurate and effective Riemann–Caputo (RC) Riemann–Liouville (RL) portraying motion. This paper focuses on a nonlinear ML-fractional system with distributed lag integral control. Employing fixed-poi...

This paper aims to study the existence and uniqueness of solution for nonlocal multiorder implicit differential equation involving Hilfer fractional derivative on unbounded domains a , ∞ ≥ 0 , in an applicable Banach...

In this paper, we define multi-normed spaces, and investigate some properties of multi-bounded mappings on multi-normed spaces. Moreover, we prove a generalized Hyers– Ulam–Rassias stability theorem associated to the Cauchy additive equation for mappings from linear spaces into multi-normed spaces.