Summary: The basic theory for a class of initial value problems for some fractional differential equation involving Riemann-Liouville differential operators is discussed by employing the classical approach from the work of V. Lakshmikantham
and A. S. Vatsala
[Nonlinear Anal., Theory Methods Appl. 69, No. 8, A, 2677–2682 (2008; Zbl 1161.34001
)]. The theory of inequalities, local existence, extremal solutions, comparison result and global existence of solutions are considered.