Fractional finite time delay evolution systems and optimal controls in infinite-dimensional spaces

Abstract

This paper concerns the fractional finite time delay evolution systems and optimal controls in infinite-dimensional spaces. A suitable mild solution of the fractional finite time delay evolution systems is introduced. Using the singular version of the Gronwall inequality with finite time delay, we obtain some sufficient conditions for the existence, uniqueness and continuous dependence of mild solutions of these control systems. A formulation for the fractional Lagrange problem is introduced. The existence of optimal pairs of fractional-time-delay evolution systems is also presented. Finally, an example is given for demonstration.

The Solvability and Fractional Optimal Control for Semilinear Stochastic Systems

“…al. [19,20] discussed the existence of local and global solutions for fractional semilinear systems, and extended the results for fractional optimal control. Using fractional powers of the linear operator, the existence of fractional optimal controls for the Lagrange problem investigated in infinite dimensional reflexive Banach space [21,22,24].…”

Successive approximation and optimal controls on fractional neutral stochastic differential equations with Poisson jumps

“… derived the controllability results for a class of neutral fractional differential equations with impulsive and infinite delays. The qualitative properties of fractional dynamical system have been studied by many researchers .…”

On nonlocal problems for fractional differential equations in Banach spaces

“…For more details, one can see the monographs of Kilbas et al [6], Lakshmikantham et al [7], Miller and Ross [8], Podlubny [12]. Very recently, fractional differential equations and optimal controls in Banach spaces are studied by Balachandran et al [3,4], N'Guérékata [9,10], Mophou and N'Guérékata [11], Wang et al [13][14][15][16][17][18][19][20], Zhou et al [22][23][24] and etc.…”