In this paper, we are concerned with a class of nonlinear implicit fractional di?erential equation adiscrete delay. By means the contraction mapping principle, prove existence unique solution.Then, investigate continuous dependence solution upon initial delay data and Ulamstability.

We consider the Cauchy problem for a degenerate fractional conservation laws driven by noise. In particular, making use of an adapted kinetic formulation, result existence and uniqueness solution is established. Moreover, unified framework also established to develop continuous dependence theory. More precisely, we demonstrate $$L^1$$ -continuous estimates on initial data, order Laplacian, diff...

The purpose of this paper is to investigate the existence and uniqueness mild solutions a semilinear Cauchy problem for an abstract fractional differential equation with state dependent nonlocal condition. Continuous dependence on initial conditions local ????-approximate solution considered will be discussed.

We consider a class of evolutionary variational inequalities arising in quasistatic frictional contact problems for linear elastic materials. We indicate sufficient conditions in order to have the existence, the uniqueness and the Lipschitz continuous dependence of the solution with respect to the data, respectively. The existence of the solution is obtained using a time-discretization method, ...

We consider an existence theorem for controi systems whose state variables for every t are in C, the set of continuous functions varying over a given set L The dependence of the state variables upon a ~ / i s induced by their dependence upon the initial state and the state equation governing the system. In contrast, the control u ---u(t) is taken as a measurable function of t alone. The usual s...