Related papers: Existence and stability analysis of solution for f…
We establish the stability of higher-order linear non-homogeneous Cauchy-Euler dynamic equations on time scales in the sense of Hyers and Ulam. That is, if an approximate solution of a higher-order Cauchy-Euler equation exists, then there…
We consider a second-order equation of Duffing type. Bounds for the derivative of the restoring force are given which ensure the existence and uniqueness of a periodic solution. Furthermore, the unique periodic solution is asymptotically…
This work deals with the finite time stability of generalized proportional fractional systems with time delay. First, based on the generalized proportional Gr\"onwall inequality, we derive an explicit criterion that enables the system…
In this paper, we obtain results on exponential stability of second order delay differential equations, which are based on a version of the Floquet theory for delay differential equations of the second order we proposed. Our version allows…
This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative…
In this paper, the stability of $\theta$-methods for delay differential equations is studied based on the test equation $y'(t)=-A y(t) + B y(t-\tau)$, where $\tau$ is a constant delay and $A$ is a positive definite matrix. It is mainly…
In this paper, by means of Banach fixed point theorem, we investigate the existence and Ulam--Hyers--Rassias stability of the non-instantaneous impulsive integrodifferential equation by means of $\psi$-Hilfer fractional derivative. In this…
In this paper, we achieve the general solution and the generalized Hyers-Ulam-Rassias stability for the quadratic type functional equation &f(x+y+2cz)+f(x+y-2cz)+c^2f(2x)+c^2f(2y) &=2[f(x+y)+c^2f(x+z)+c^2f(x-z)+c^2f(y+z)+c^2f(y-z)] {2.6 cm}…
In this letter we are concerned with the possibility to approach the existence of solutions to a class of discontinuous dynamical systems of fractional order. In this purpose, the underlying initial value problem is transformed into a…
The first order difference equation induced by the sequence of maps on $ \mathbb{C} $ has Hyers-Ulam stability where the limit of the geometric average of growth rate is convergent and not equal to one. %The average growth rate is a…
We study differential equations with a linear, path dependent drift and discrete delay in the diffusion term driven by a $\gamma$-H\"older rough path for $\gamma > \frac{1}{3}$. We prove well-posedness of these systems and establish a…
This study presents new estimates for fractional derivatives without singular kernels defined by some specific functions. Based on obtained inequalities, we give a useful method to establish the global stability of steady states for…
In this paper, using the Riemann-Liouville fractional integral with respect to another function and the $\psi-$Hilfer fractional derivative, we propose a fractional Volterra integral equation and the fractional Volterra integro-differential…
For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions…
We clarify the Hyers--Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, in the case of a specific time scale with two alternating step sizes, where the exponential function changes…
In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite…
An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
This paper considers linear functional equations on $\mathbb R^d$ with distributed delays defined by matrix-valued measures of bounded variation. More precisely, we are interested in providing conditions to ensure that the exponential…
By means of two fractional order integral inequalities we investigate the existence and uniqueness of the solutions of the fractional nonlinear Volterra integral equation and a fractional nonlinear integrodifferential equation in Banach…