Existence and Uniqueness for Parabolic Problems with Caputo Time Derivative

In this paper we are interested in the well-posedness of fully nonlinear Cauchy problems in which the time derivative is of Caputo type. We address this question in the framework of viscosity solutions, obtaining the existence via Perron s method, and comparison for bounded sub and supersolutions by a suitable regularization through inf and sup convolution in time. As an application, we prove the steady-state large time behavior in the case of proper nonlinearities and provide a rate of convergence by using the Mittag–Leffler operator. © 2017 Elsevier Inc.