In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

‎In this paper‎, ‎we present the‎ generalized hyperstability results of cubic functional equation in‎ ‎ultrametric Banach spaces using the fixed point method‎.

and Applied Analysis 3 In 2008, Gordji et al. 17 provided the solution as well as the stability of a mixed type cubic-quartic functional equation. We only mention here the papers 19, 32, 33 concerning the stability of the mixed type functional equations. In this paper, we deal with the following general cubic-quartic functional equation: f ( x ky ) f ( x − ky) k2(f(x y) f(x − y)) 2 ( 1 − k2 ) f...

We consider the small time semi-classical limit for nonlinear Schrödinger equations with defocusing, smooth, nonlinearity. For a super-cubic nonlinearity, the limiting system is not directly hyperbolic, due to the presence of vacuum. To overcome this issue, we introduce new unknown functions, which are defined nonlinearly in terms of the wave function itself. This approach provides a local vers...