New local perturbation bounds are obtained for the continuous-time H∞-optimization problem, which are nonlinear functions of the data perturbations and are tighter than the existing condition number based local bounds. The nonlinear local bounds are then incorporated into nonlocal perturbation bounds which are less conservative than the existing nonlocal perturbation estimates for the H∞-optimi...

This paper is first study for considering nonlocal elliptic equation with Caputo derivative. We obtain the upper bound of mild solution. The second contribution to provide lower solution at terminal time. prove non-correction problem in sense Hadamard. main tool use and bounds Mittag-Lefler function, combined analysis Hilbert scales space.

The solvability conditions for a class of boundary value problems nonlocal biharmonic equation in the unit ball with Neumann on are studied. nonlocality is generated by some orthogonal matrix. presence and uniqueness solution to proposed condition examined, an integral representation Dirichlet problem terms Green's function obtained. First, auxiliary statements established: given, this written,...