Maximal Lp−regularity of two–term fractional differential equations with boundary conditions

Abstract

In this paper, we consider two-term fractional differential equations (FDEs) with boundary conditions. We use operator techniques including Fourier multipliers, perturbation theory of operators, the trace theorem, and Green\"s functions to establish maximal regularity of three types of FDEs with nonlocal or Dirichlet boundary conditions in Lp-space. As an application, the existence-uniqueness and coercive estimate of the Cauchy problem for fractional parabolic differential equation are given.