Asymptotic behavior of solutions to time fractional neutral functional differential equations

Abstract In this paper, we derive a new fractional Halanay-like inequality, which is used to characterize the long-term behavior of time fractional neutral functional differential equations (F-NFDEs) of Hale type with order α ∈ ( 0 , 1 ) . The contractivity and dissipativity of F-NFDEs are established under almost the same assumptions as those for classical integer-order NFDEs. In contrast to the exponential decay rate for NFDEs, the F-NFDEs are proved to have a polynomial decay rate. The numerical scheme based on the L 1 method together with linear interpolation is constructed and applied in several examples to illustrate the theoretical results and to reveal the quite different long-term decay rate in the solutions between F-NFDEs and NFDEs.