Existence and uniqueness results for a nonlinear singular fractional differential equation of order σ ∈ (1,2)

Abstract

The first objective of this article is to discuss the local existence of the solution to an initial value problem involving a non-linear differential equation in the sense of Riemann-Liouville fractional derivative of order c e (1,2), when the nonlinear term has a singularity at zero of its independent argument. Hereafter, by using some tools of Lebesgue spaces such as Holder inequality, we obtain Nagumo-type, Krasnoselskii-Krein-type and Osgood-type uniqueness theorems for the problem.