This paper is devoted to investigating one type of nonlinear two-term fractional order delayed differential equations involving Caputo derivatives. The Leray–Schauder alternative fixed-point theorem and Banach contraction principle are applied analyze the existence uniqueness solutions problem with infinite delay. Additionally, Hyers–Ulam stability considered for delay conditions.

We show that generalizations of some (classical) results on the Hyers-Ulam stability of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable.

We prove the generalized Hyers-Ulam-Rassias stability of a partitioned functional equation. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with partitioned functional equations in Banach algebras.

The Hyers-Ulam stability of the generalized trigonometric-quadratic functional equation ( ) ( ) ( ) ( ) ( ) ( ) 2 F x y G x y H x K y L x M y + − − = + + over the domain of an abelian group and the range of the complex field is established based on the assumption of the unboundedness of the function K. Subject to certain natural conditions, explicit shapes of the functions H and K are determine...

We survey the recent results concerning the applications of power series method to the study of Hyers–Ulam stability of differential equations.

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 ...