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...

Tension-Leg Platform (TLP) is a vertically moored floating structure. The platform is permanently mooredby tendons. Surge equation of motion of TLP is highly nonlinear because of large displacement and it should be solved with perturbation parameter in time domain. This paper compare the dynamic motion responses of a TLP in regular sea waves obtained by applying three method in time domain usin...

High-order uncertain differential equations are applied to model differentiable uncertain systems with high-order differentials. In order to describe the influence of the initial value on the solution, this paper proposes two concepts of stability for high-order uncertain differential equation, including stability in measure and stability in mean. Most important of all, some stability theorems ...

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, a new numerical method for solving the fractional Riccati differential  equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon  fractional-order Bernoulli functions approximations. First, the  fractional-order Bernoulli functions and  their properties are  presented. Then, an operational matrix of fractional order integration...