Optimal control of fractional diffusion equation

Approximate Controllability for Functional Equations with Riemann-Liouville Derivative by Iterative and Approximate Method

“…On the other hand, the notion of controllability plays a central role in the study of the theory of control and optimization. Therefore, there are a lot of works on the controllability, approximate controllability, and optimal control of linear and nonlinear differential and integral systems in various frameworks (see [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and references therein).…”

On the existence of mild solutions to the Cauchy problem for a class of fractional evolution equation

“…The fractional evolution equations have received increasing attention during recent years and have been studied extensively (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13] and references therein) since they can be used to describe many phenomena arising in engineering, physics, economy, and science.…”

“…We mention that much of the previous research on the evolution equations was done provided that the operator in the linear part is the infinitesimal generator of a strongly continuous operator semigroup, an analytic semigroup, or a compact semigroup, or is a Hille-Yosida operator (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12]14,15] and references therein). On the other hand, when the operator in the linear part is an almost sectorial operator, for which the resolvent operators do not satisfy the required estimate to be a sectorial operator (see the example of almost sectorial operators which are not sectorial given by von Wahl in [16]), much less is known about the fractional evolution equations of neutral type with almost sectorial operators.…”

A Spectral Method for Optimal Control Problems Governed by the Time Fractional Diffusion Equation with Control Constraints

“…More recently, Mophou [15] applied the classical control theory to a fractional diffusion equation, involving a Riemann-Liouville fractional time derivative. The existence and uniqueness of the solution were established.…”