分数阶中立型时滞微分方程解的存在性及指数估计

The existence and exponential estimate for the solution to the fractional neutral differential equation with time delay

近年来,随着分数阶微分方程在众多领域的广泛应用,其理论研究也引起了国内外学者的关注.论文研究分数阶中立型时滞微分方程在解存在的前提下其解的指数估计.首先,由分步法讨论分数阶中立型时滞微分方程的解的存在唯一的条件;然后,在解存在的前提下,利用Gronwall不等式,给出分数阶中立型时滞微分方程解的指数估计.

Abstract. In recent years, fractional differential equation with time delay has played an important role in many fields and the theory of fractional differential equation has drawn much attention of scholars. The exponential estimate of solution to the fractional neutral differential equation was derived under suitable conditions. First, using step by step method, the existence and uniqueness of the solution to fractional neutral differential equation with time delay exponential was discussed. Then, in the condition of the existence of the solution, the estimation was given by Gronwall inequality.