Solutions of linear uncertain fractional order neutral differential equations

•The concept of uncertain fractional neutral differential equations is proposed•Provide the analytic solution of a type of linear uncertain fractional neutral differential equations.•Provide the inverse uncertainty distribution of the solution.•Investigate the dependence of the solution on initial function. Uncertain fractional order neutral differential equation is an important model to describe the evolution process of uncertain dynamical system. This paper devotes to studying linear uncertain fractional order neutral differential equations. After providing the analytic solutions for linear uncertain fractional order neutral differential equations by the Mittag-Leffler function, the author investigates the inverse uncertainty distribution of the solution to linear uncertain fractional order neutral differential equation by the α-path and has a discussion of the dependence of the solution on initial function based on the generalized Gronwall inequality.