Upper and lower estimates for the separation of solutions to fractional differential equations

Abstract Given a fractional differential equation of order $$\alpha \in (0,1]$$ α ∈ ( 0 , 1 ] with Caputo derivatives, we investigate in quantitative sense how the associated solutions depend on their respective initial conditions. Specifically, look at two $$x_1$$ x and $$x_2$$ 2 , say, same equation, both which are assumed to be defined common interval [0, T ], provide upper lower bounds for difference $$x_1(t) - x_2(t)$$ t ) - all $$t [0,T]$$ [ T that stronger than previously described literature.