We prove the generalized Hyers--Ulam stability  of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.

In this paper, we introduce the notion of geometric Riemann scheme of the sixth Painlevé equation, which consists of the pair of accessible singular points and matrix of linear approximation around each singular point on the boundary divisor in the Hirzebruch surface. Giving this in the differential system satisfying certain conditions, we can recover the Painlevé VI system with the polynomial ...

This paper presents a generalization for systems of partial differential equations of Gronwall's classical integral inequality for ordinary differential equations. The proof is by reducing the vector integral inequality to a vector partial differential inequality and then using a vector generalization of Riemann's method to obtain the final inequality. The final inequality involves a matrix fun...

In this paper, the (3+1)-dimensional BKP equation is mainly being discussed. Based on the the Wronskian technique and the Pfaffian properties, Wronskian and Grammian solutions have been established. Generating functions for matrix entries satisfy linear system of partial differential equations involving a free parameter.

Wronskian and Grammian formulations are established for a (3 + 1)-dimensional generalized KP equation, based on the Plücker relation and the Jacobi identity for determinants. Generating functions for matrix entries satisfy a linear system of partial differential equations involving a free parameter. Examples of Wronskian and Grammian solutions are computed and a few particular solutions are plo...

In this paper, we study the complete synchronization of a class of time-varying delayed coupled chaotic systems using feedback control. In terms of Linear Matrix Inequalities, a sufficient condition is obtained through using a Lyapunov-Krasovskii functional and differential equation inequalities. The conditions can be easily verified and implemented. We present two simulation examples to illust...

Abstract We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by splitting space domains. However, we take into account approximation errors during stability analysis. Using a quadratic Lyapunov function, we obtain a suff...

 In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an IVP of first order hybrid  random differential equations with the linear perturbation of second type. A comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential eq...

This paper addresses the H , fixed-lag smoothing and prediction problems for linear continuous-time systems. We first present a solution to the optimal HZ estimation problem for linear continuous-time systems with instantaneous and delayed measurements. It is then shown that the H , fixedlag smoothing and prediction problems can be converted to the latter problem in Krein space. Therefore, the ...

In this paper any non-homogeneous differential equation with constant coefficients is reduced to a matrix equation ~q = ~cP . For the discussion, ~q represents a matrix of constant coefficients to the differential equation, ~c a matrix of arbitrary constants to the solution, and P is a lower triangular matrix with entries that are derivatives of the characteristic polynomial of the differential...