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In this study, we pay attention to a functional differential equation (FDE) of first order including N-variable delays. We construct new sufficient conditions in relation to the Hyers-Ulam stability (HUS) and the generalized Hyers-Ulam-Rassias stability (GHURS) of the FDE of first order including N-variable delays. By using Banach contraction principle (BCP), Picard operator and Gronwall's lemma, we confirm two new theorems with regard to the HUS and the GHURS. The results of this study are new, they extend and improve some earlier results of the HUS and the GHURS. [ABSTRACT FROM AUTHOR]

In this article, admissibility problem for a kind of singular systems with delays is studied. Firstly, the given singular system with delays is transformed into a neutral system with delays. Secondly, new sufficient criteria are obtained on the stability of the new neutral system by aid of Wirtinger-based integral inequality, linear matrix inequality (LMI) and suitable Lyapunov-Krasovskii functionals (LKFs). The obtained criteria are valid for both of the systems. At the end, two numerical examples are given to illustrate the applicability of the obtained results using MATLAB-Simulink software. By this article, we extend and improve some results of the past literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear differential system of fractional-order with multiple variable delays. We investigate asymptotic stability of zero solution of the considered system. We prove a new result, which includes sufficient conditions, on the subject by means of a suitable Lyapunov functional. An example with numerical simulation of its solutions is given to illustrate that the proposed method is flexible and efficient in terms of computation and to demonstrate the feasibility of established conditions by MATLAB-Simulink. [ABSTRACT FROM AUTHOR]

This study is concerned with the existence, uniqueness and global exponential stability of weighted pseudo almost periodic solutions of a generalized Nicholson’s blowflies equation with mixed delays. Using some differential inequalities and a fixed point theorem, sufficient conditions were obtained for the existence, uniqueness of at the least a weighted pseudo almost periodic solutions and global exponential stability of this solution. The results of this study are new and complementary to the previous ones can be found in the literature. At the end of the study an example is given to show the accuracy of our results. [ABSTRACT FROM AUTHOR]

The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases. [ABSTRACT FROM AUTHOR]

The aim of this paper is first to investigate the stability of the zero solution to a new Liénard type equation with multiple variable delays by two different methods. The methods to be used in the proofs involve the Lyapunov-Krasovskiĭ functional approach and the fixed point technique under an exponentially weighted metric, respectively. We make a comparison between the applications of these methods with the established conditions on the same stability problems. Then, we obtain three new results for uniformly stability and boundedness/uniformly boundedness of the solutions to the considered equation by the Lyapunov-Krasovskiĭ functional approach. An example is given to verify the results obtained by the Lyapunov-Krasovskiĭ functional approach. Our results complement and improve some recent ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we give some criteria to ensure the global existence and boundedness of solutions to a kind of third order nonlinear vector differential equations. By using the Lyapunov's direct method, we obtain a new result on the topic and give an example for the illustrations. Our result includes, completes and improves some earlier results in the literature. [ABSTRACT FROM AUTHOR]

This paper investigates the instability of the zero solution of a certain vector differential equation of the sixth order with delay. Using the Lyapunov-Krasovskii functional approach, we obtain a new result on the topic and give an example for the related illustrations [ABSTRACT FROM AUTHOR]

This paper proposes two models of a general nonlinear within-host Chikungunya virus (CHIKV) dynamics. The production, incidence, proliferation and removal rates of all compartments are modeled by general nonlinear functions that satisfy a set of reasonable conditions. The second model takes into consideration two forms of infected host cells: (i) latently infected cells which do not produce the CHIKV, (ii) actively infected cells which generate the CHIKV particles. We show that all the solutions of the models are nonnegative and bounded. The global stability of the steady states of the models is proven by applying Lyapunov method and LaSalle’s invariance principle. We perform numerical simulations to complement the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the conformable fractional Volterra integral equation. We study the existence of a resolvent kernel corresponding to conformable fractional Volterra integral equation. The technique of proof involves Lebesgue dominated convergence theorem. Our results improve and extend the results obtained in literature. [ABSTRACT FROM AUTHOR]

Semiconductor quantum dots (QDs) have unique atom-like properties. In this work, the electronic states of InAs quantum dot grown on a GaAs substrate has been studied. The analytical expressions of electron wave function for cone-like quantum dot on the semiconductor surface has been obtained and the governing eigen value equation has been solved, thereby obtaining the dependence of ground state energy on radius and height of the cone-shaped nano-dots. In addition, the energy of eigenvalues is computed for various length and thickness of the wetting layer (WL). We discovered that the eigen functions and energies are nearly associated with the GaAs potential. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effects of nonlinear behaviour of the dimensionless concentrations of the ethanol and acetaldehyde in a fixed bed laboratory reactor. The work is based on solving the nonlinear differential equation of concentration of the ethanol and acetaldehyde by means of the He’s variational iteration method (VIM). Also, the numerical simulation (4th order Runge – Kutta method) is reported using Matlab software. The analytical solutions are compared with numerical results in order to achieve conclusions based on not only for accuracy and efficiency of the solutions, but also the simplicity of the taken procedures which would have remarkable effects on the time devoted for solving process. The analytical result reported in this work is useful to understand the behaviour of the system. Furthermore, due to the accuracy and convergence of obtained solutions, it is proved that the VIM could be applied through other nonlinear problems even with high nonlinearity. [ABSTRACT FROM AUTHOR]