We consider an optimal rearrangement maximization problem involving the fractional Laplace operator ( − Δ ) s , 0 < 1 and Gagliardo-Nirenberg seminorm [ u ] . prove existence of a maximizer, analyze its properties show that it satisfies unstable obstacle equation for some α > = χ { }

In this paper, a finite-horizon optimal control problem involving dynamical system described by linear Caputo fractional differential equation and quadratic cost functional is considered. An explicit formula for the value given, which includes solution of certain Fredholm integral equation. A step-by-step feedback procedure constructing $ \varepsilon $-optimal controls with any accuracy &gt; 0 ...

The existence of a unique strong solution for the Cauchy problem to semilinear nondegenerate fractional differential equation and for the generalized Showalter–Sidorov problem to semilinear fractional differential equation with degenerate operator at the Caputo derivative in Banach spaces is proved. These results are used for search of solution existence conditions for a class of optimal contro...

Recently, there has been significant development in the existence of mild solutions for fractional semilinear integro-differential equations but optimal control is not provided. The aim of this paper is studying optimal feedback control for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators ...

in this paper we present a new method for solving fractional optimal control problems with delays in state and control. this method is based upon bernstein polynomial basis and using feedback control. the main advantage of using feedback or closed-loop controls is that they can monitor their effect on the system and modify the output accordingly. in this work, we use bernstein polynomials to tr...