Analysis of Direct and Inverse Problems for a Fractional Elastoplasticity Model

This study is devoted to a nonlinear time fractional inverse coeficient problem. The unknown coefficient depends on the gradient of the solution and belongs to a set of admissible coefficients. First we prove that the direct problem has a unique solution. Afterwards we show the continuous dependence of the solution of the corresponding direct problem on the coefficient, the existence of a quasi-solution of the inverse problem is obtained in the appropriate class of admissible coefficients.