Hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior‎. ‎The hybrid differential equations have a wide range of applications in science and engineering‎. ‎The hybrid systems are devoted to modeling‎, ‎design‎, ‎and validation of interactive systems of computer programs and continuous systems‎. ‎Hybrid fuzzy differential equations (HFDEs) is considered by ...

distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper we study numerical methods for hybrid fuzzy differential equations by an appllication of the Milne's fourth order predictor-corrector method for fuzzy differential equations. We prove a conv...

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.

The π-derivative for fuzzy function is considered. Consequently, using this π-derivative we study fuzzy differentuial equations. In particular, we build a solution for a fuzzy differential equation with the help of a system of ordinary differential equations which is generates of the π-derivative. Keywords— π-derivative for set valued functions, derivative for fuzzy functions, fuzzy differentia...

hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior‎. ‎the hybrid differential equations have a wide range of applications in science and engineering‎. ‎the hybrid systems are devoted to modeling‎, ‎design‎, ‎and validation of interactive systems of computer programs and continuous systems‎. ‎hybrid fuzzy differential equations (hfdes) is considered by ...

In this study the interaction between self-excited and paramet rically excited oscillations in two-degree-of-freedom systems with quadratic nonlinearities is investigated. The fundamental parametric resonance of the first mode and 3:1 internal resonance is considered, followed by 1:2 internal and parametric resonances of the second mode. The method of multiple time scales is applied to derive f...

in this paper, a  fuzzy numerical procedure for solving fuzzy linear volterra integro-differential equations of the second kind under strong  generalized differentiability is designed. unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2times 2$ system ofcrisp equations, that is the main difference between our method  and other numerical methods.error ana...