This paper deals with the existence, uniqueness, and Ulam-stability outcomes for $\Xi$-Hilfer fractional fuzzy differential equations impulse. Further, by using techniques of nonlinear functional analysis, we study Ulam-Hyers-Rassias stability.

In this paper, we solve the additive ρ -functional inequalities ‖ f (x+ y)− f (x)− f (y)‖ ∥∥∥ρ ( 2 f ( x+ y 2 ) − f (x)− f (y) ∥∥∥ (0.1) and ∥∥∥2 f ( x+ y 2 ) − f (x)− f (y) ∥∥∥ ‖ρ ( f (x+ y)− f (x)− f (y))‖ , (0.2) where ρ is a fixed non-Archimedean number with |ρ| < 1 . Furthermore, we prove the Hyers-Ulam stability of the additive ρ -functional inequalities (0.1) and (0.2) in non-Archimedean...

In this paper, we study the Hyers-Ulam stability problem for the following functional equation (E(K)) ∑ φ∈Φ ∫ K f(xkφ(y)k)dωK(k) = |Φ|f(x)g(y), x, y ∈ G, where G is a locally compact group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g : G −→ C are continuous complex-valued functions such that f satisfies the Kan...

If the answer is affirmative, the functional equation for homomorphisms is said to be stable in the sense of Hyers and Ulam because the first result concerning the stability of functional equations was presented by Hyers. Indeed, he has answered the question of Ulam for the case where G1 and G2 are assumed to be Banach spaces (see [8]). We may find a number of papers concerning the stability re...

&lt;abstract&gt;&lt;p&gt;We prove existence and uniqueness of solutions to discrete fractional equations that involve Riemann-Liouville Caputo derivatives with three-point boundary conditions. The results are obtained by conducting an analysis via the Banach principle Brouwer fixed point criterion. Moreover, we stability, including Hyers-Ulam Hyers-Ulam-Rassias type results. Finally, some numer...

In 1940, Ulam [1] proposed the following stability problem: “When is it true that a function which satisfies some functional equation approximatelymust be close to one satisfying the equation exactly?” Next year, Hyers [2] gave an answer to this problem for additive mappings between Banach spaces. Furthermore, Aoki [3] and Rassias [4] obtained independently generalized results of Hyers’ theorem...

In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of the following Cauchy-Jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem t...

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 are going to study the Hyers{Ulam{Rassias typesof stability for nonlinear, nonhomogeneous Volterra integral equations with delayon nite intervals.