Identification problem of a fractional thermoelastic deformation system with incomplete data: A sentinel method
In this work, the problem of the deformations for fractional coupled thermoelastic systems is formulated and solved by Riemann Liouville and Caputo fractional derivatives. In this work, the problem of the deformations for fractional coupled thermoelastic systems is formulated and solved by Riemann Liouville and Caputo fractional derivatives. The initial conditions and some boundary conditions are partially known, thus the problem studied here is an inverse problem with incomplete data. The initial conditions are understood here in the left Riemann-Liouville fractional integrals sense. Our purpose is to estimate unknown boundary conditions of the transverse displacement since the other missing terms in the initial conditions are of no interest to us. We base our estimates on the measured temperature in a small observatory domain. We look for the desired sentinel function which will obviously lead to study the null controllability problem. The right Caputo fractional derivative is more suitable to introduce the fractional coupled adjoint state systems. The identification problem with the Riemann Liouville and Caputo fractional derivatives senses suggested in this work is the generalization of classical identification problems in the no fractional case.