Identification problem of a fractional thermoelastic deformation system with incomplete data: A sentinel method

Abstract

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.