Asymptotic Constancy for the Solutions of Caputo Fractional Differential Equations with Delay

In this paper, we aim to study the neutral-type delayed Caputo fractional differential equations of form CDαxt−gt,xt=ft,xt,t∈t0,∞,t0≥0 with order 0<α<1, which can be used describe growth processes in real-life sciences at present depends on not only past state but also rate. Our ultimate goal is concentrate convergence solutions a predetermined constant by establishing linkage between equation and an integral equation. our analysis, sufficient conditions for asymptotic results are obtained due fixed point theory. The utilization contraction mapping principle convenient approach obtaining technical that guarantee constancy solutions.