Numerical Solutions of Direct and Inverse Problems for a Time Fractional Viscoelastoplastic Equation

This paper is devoted to numerical solutions of direct and inverse problems for the nonlinear nonlocal time fractional equation /tu(x,y,t)-delta[f(T2)delta u]=2t, where T2=|delta u|2. After solving the direct problem by the method of lines, a numerical method based on discretization of the minimization problem, steepest descent method, and least-squares approach is proposed for the solution of the inverse problem. Numerical examples with noise-free and noisy data illustrate applicability and accuracy of the proposed method to some extent. (C) 2017 American Society of Civil Engineers.