Existence and optimal control of Hilfer fractional evolution equations

Abstract

This article investigates the existence and optimal controls for a class of Hilfer fractional evolution equations of order in (0,1)\left(0,1) with type of [0,10,1]. The first part focuses on analyzing the existence and uniqueness of the mild solution using the fixed point theorem and semigroup theory. In the second part, an optimal control problem that admits an optimal pair is considered. Furthermore, the necessary optimality conditions for an optimal control problem governed by semilinear fractional diffusion equations are presented.

Keywords

• existence
• uniqueness
• optimal control
• fractional evolution equations
• hilfer derivative
• 49j20
• 49k20
• 35r11
• 26a33