Variational Lyapunov method for fractional differential equations

In this paper the variational Lyapunov method is developed for Caputo fractional differential equations. Further, the comparison theorems are proved with a relaxed hypothesis: the assumption of local Holder continuity is relaxed to CpCp continuity of the functions involved in the Riemann–Liouville fractional differential equations. In this process the Grünwald–Letnikov derivative is used to define Dini derivatives. Also, a relation between ordinary and fractional differential equations is given.