This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: { D t x(t) = f(t, x(t), D β t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = ∫ 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle. Keywords—Fractional differential equation; Integral boundary condi...

This paper studies the artificial outflow boundary condition for Navier-Stokes system. type of is widely used and it therefore very important to study its influence on a numerical solution corresponding boundary-value problem. We particularly focus role coefficient in front nonlinear term outflow. The this examined numerically, comparing obtained results close neighbourhood experiment carried o...

This paper deals with a one-dimensional wave equation nonlinear dynamic boundary condition and Neumann-type control acting on the other extremity. We consider class of stabilizing feedbacks that only depend velocity at controlled The uncontrolled is subject to first-order term, which may represent anti-damping. Initial data taken in optimal energy space associated problem. Exponential decay mec...