A study for a higher order Riemann-Liouville fractional differential equation with weakly singularity

Abstract

In this paper, we study an initial value problem with a weakly singular nonlinear fractional differential equation of higher order. First, we establish the existence of global solutions to the problem within the appropriate function space. We then introduce a generalized Riemann-Liouville mean value theorem. Using this theorem, we prove the Nagumo-type uniqueness theorem for the stated problem. Moreover, we give two examples to illustrate the applicability of the existence and uniqueness theorems.

Keywords

• weakly singular integral equation
• fractional differential equation
• initial value problem
• global existence