If function y=f(x) has a derivative in the point x: The existing function derivative f’ (x) in point x and the function increment representation in the form ∆y=A*∆x+α(∆x)*∆x are equivalent features of ...

Abstract: In this paper, using the concept of horizontal membership functions, a new definition of fuzzy derivative called granular derivative is proposed based on granular difference. Moreover, a new ...

It is well known that Malliavin calculus can be applied to a stochastic differential equation with Lipschitz continuous coefficients in order to clarify the existence and the smootheness of the ...