and Applied Analysis 3 Moreover, Bourgin 15 and Găvruţa 16 have considered the stability problem with unbounded Cauchy differences see also 17–27 . On the other hand, J. M. Rassias 28–33 considered the Cauchy difference controlled by a product of different powers of norm. However, there was a singular case; for this singularity a counterexample was given by Găvruţa 34 . This stability phenomeno...

In this paper we introduce a notion of a non-Archimedean fuzzy norm and study the stability of the Cauchy equation in the context of non-Archimedean fuzzy spaces in the spirit of Hyers–Ulam–Rassias–Găvruţa. As a corollary, the stability of the Jensen equation is established. We indeed present an interdisciplinary relation between the theory of fuzzy spaces, the theory of non-Archimedean spaces ...

In this current paper, using q-fractional calculus, we study the Duffing–Rayleigh type problem with sequential fractional q-derivative of Caputo type. We investigate existence and uniqueness solutions by applying some classical fixed point theorems. Also define Ulam–Hyers Ulam–Hyers–Rassias stabilities for our problem. An example is presented to illustrate main results.

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...

The Laplace transform method is applied to study the semi-Hyers–Ulam–Rassias stability of a Volterra integro-differential equation second order. A general formulated first; then, some particular cases for function from kernel are considered.

Abstract This article discusses the stability results for solution of a fractional q -integro-differential problem via integral conditions. Utilizing Krasnoselskii’s, Banach fixed point theorems, we demonstrate existence and uniqueness results. Based on obtained, conditions are provided to ensure generalized Ulam Ulam–Hyers–Rassias stabilities original system. The illustrated by two examples.

Copyright q 2010 Dongseung Kang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate the generalized Hyers-Ulam-Rassias stability problem in quasi-β-normed spaces and then the stability by using a subadditive function f...

The aim of this paper is to consider the Hyers-Ulam stability of a class of parabolic equation { ∂u ∂t − a 2∆u+ b · ∇u+ cu = 0, (x, t) ∈ Rn × (0,+∞), u(x, 0) = φ(x), x ∈ Rn. We conclude that (i) it is Hyers-Ulam stable on any finite interval; (ii) if c 6= 0, it is Hyers-Ulam stable on the semi-infinite interval; (iii) if c = 0, it is not Hyers-Ulam stable on the semi-infinite interval by using ...

Problem 1.1. Given a metric group (G,·,d), a positive number ε, and a mapping f : G→ G which satisfies the inequality d( f (xy), f (x) f (y)) ≤ ε for all x, y ∈ G, do there exist an automorphism a of G and a constant δ depending only on G such that d(a(x), f (x)) ≤ δ for all x ∈G? If the answer to this question is affirmative, we say that the equation a(xy) = a(x)a(y) is stable. A first answer ...

n this paper we study the Hyers-Ulam-Rassias stability of Cauchyequation in Felbin's type fuzzy normed linear spaces. As a resultwe give an example of a fuzzy normed linear space such that thefuzzy version of the stability problem remains true, while it failsto be correct in classical analysis. This shows how the category offuzzy normed linear spaces differs from the classical normed linearspac...