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 L1 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.