In the current manuscript, we study uniqueness and Ulam-stability of solutions for sequential fractionalpantograph differential equations with nonlocal boundary conditions. The is es-tablished by Banach's fixed point theorem. We also define Ulam-Hyers stability theUlam-Hyers-Rassias mentioned problem. An example presented to illustrate main results.

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.

Stability is the most relevant property of dynamical systems. The stability stochastic differential equations a challenging and still open problem. In this article, using fuzzy Mittag–Leffler function, we introduce new controller function to stabilize equation (SDE) ν′(γ,μ)=Fγ,μ,ν(γ,μ). By adopting fixed point technique, are able prove Mittag–Leffler–Hyers–Ulam–Rassias SDE.

<p style='text-indent:20px;'>In this paper, the Hyers-Ulam-Rassias stability of high-dimensional quaternion fuzzy dynamic equations with impulses is first considered on time scales. Some fundamental calculus results functions in space are established. Based it, some sufficient conditions obtained to guarantee impulsive case. Moreover, several examples provided show feasibility our main va...

Cădariu and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we adopt the idea of Cădariu and Radu to prove the Hyers-Ulam-Rassias stability of a functional equation of the square root spiral, f (√ r2 + 1 ) = f(r)+ tan−1(1/r).

In this paper, using the direct method we study the generalized Hyers-Ulam-Rassias stability of the following quadratic functional equations (2 ) ( ) 6 ( )     f x y f x y f x and (3 ) ( ) 16 ( )     f x y f x y f x for the mapping f from normed linear space in to 2-Banach spaces.

We introduce three reasonable versions of fuzzy approximately additive functions in fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in a fuzzy sense. © 2007 Elsevier B.V. All rights reserved. MSC: primary 46S40secondary 39B52 39B82 26E50 46S50

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.

In this paper, we will consider Hyers–Ulam–Rassias stability of multipliers and ring derivations between Banach algebras. As a corollary, we will prove superstability of ring derivations and multipliers. That is, approximate multipliers and approximate ring derivations are exact multipliers and ring derivations.