Weighted fractional neutral functional differential equations

In this paper, we consider a weighted neutral functional differential equation of fractional order $0<\alpha <1$, with nonzero initial values, infinite delay, and the standard Riemann–Liouville fractional derivative. By using a variety of tools of fractional calculus including the Schauder fixed point theorem and the Banach fixed point theorem, we verify the existence, uniqueness and continuous dependence of solution of weighted neutral problem.