Initial‐boundary value problem for a multiterm time‐fractional differential equation and its application to an inverse problem

Abstract

In this paper, we deal with the multiterm time‐fractional partial differential equation involving the Caputo operator associated with the Laplace operator, which includes the momentum equations of the fractional Oldroyd‐B fluid and the fractional Burgers fluid under some suitable conditions. By using several properties of multivariate Mittag–Leffler functions, the well‐posedness and the long‐time behavior for the Dirichlet problem are obtained. In addition, the uniqueness in inverse problem of determining orders of time‐fractional derivatives of the equation is proved.