Solvability of a solution and controllability of partial fractional differential systems

Abstract

The paper is devoted to study the solvability of a solution for a Dirichlet problem for a class of time-fractional partial parabolic differential system, by using the energy inequality method for the primal problem. Then, by the Tikhonov regularization method, we can study the approximate controllability of the dual problem. We were therefore able to study the solvability of a solution and controlability of this problem.

Subject Classification: (2010):

• 34K37
• 35D35
• 34A12
• 35B45
• 93B05
• 47A10
• 49J15

Keywords:

• Fractional caputo derivatives
• Strong solution
• Energy inequality
• Approximate controllability
• Optimal controls
• Regularization of Tikhonov