Implicit fractional differential equations: Existence of a solution revisited

Abstract

This paper focuses on revisiting and improving the results regarding the existence of a solution to the implicit fractional differential equations (FDEs) given in the following form: D-C(p)omega(x) = f(x, omega(x), D-C(p)omega(x)) for all x is an element of [0, T] with the initial condition x is an element of(0) = [0,T] where 0 < p < 1, D-C(p) is the Caputo fractional derivative (CFD). Mainly, we aim to weaken the necessary conditions often found in the literature for guaranteeing the existence of solution.