In this paper, we study the existence of solutions for fractional differential equations with Caputo-Hadamard derivative order 2 (1, 2]. The uniqueness result is proved via Banach’s contraction mapping principle and results are established by using Schauder’s fixed point theorem. Furthermore, Ulam-Hyers Ulam-Hyers-Rassias stability proposed equation employed. Some examples given to illustrate r...

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 1940, Ulam [13] proposed the Ulam stability problem of additive mappings. In the next year, Hyers [5] considered the case of approximately additive mappings f : E→ E′, where E and E′ are Banach spaces and f satisfies inequality ‖ f (x+ y)− f (x)− f (y)‖ ≤ ε for all x, y ∈ E. It was shown that the limit L(x) = limn→∞ 2−n f (2nx) exists for all x ∈ E and that L is the unique additive mapping s...

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...

The purpose of this article is to discuss the existence, uniqueness, and Ulam–Hyers stability solutions a coupled system fractional differential equations with Erdélyi–Kober Riemann–Liouville integral boundary conditions. Banach fixed point theorem used prove uniqueness solutions, while Leray–Schauder alternative existence solutions. Furthermore, we conclude that solution discussed problem Hyer...

We will apply the successive approximation method forproving the Hyers--Ulam stability of a linear integral equation ofthe second kind.

The aim of this work is to analyze the relative controllability and Ulamn–Hyers stability ψ-Caputo fractional neutral delay differential system. We use ψ-delayed perturbation Mitttag–Leffler matrix function Banach contraction principle examine Ulam–Hyers our considered formulate Grammian establish results linear fractonal Further, we employ fixed-point technique Krasnoselskii’s type sufficient ...

Using the Hyers-Ulam-Rassias stability method, weinvestigate isomorphisms in Banach algebras and derivations onBanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}Moreover, we prove the Hyers-Ulam-Rassias stability of homomorphismsin Banach algebras and of derivations on Banach ...

We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...