On the separation of solutions to fractional differential equations of order α ∈ (1,2)

Given the Caputo-type fractional differential equation Dαy(t)=f(t,y(t)) with α∈(1,2), we consider two distinct solutions y1,y2∈C[0,T] to this equation subject to different sets of initial conditions. In this framework, we discuss nontrivial upper and lower bounds for the difference |y1(t)−y2(t)| for t∈[0,T]. The main emphasis is on describing how such bounds are related to the differences of the associated initial values.