On the separation of solutions to fractional differential equations of order \(\alpha \in (1,2)\) (Q6577607)

This paper considers two distinct solutions to the Caputo-type fractional differential equation subject to different sets of initial conditions. Nontrivial upper and lower bounds for different initial conditions are discussed. How such bounds are related to the differences of the associated initial values is given. These results extend the theory of the initial value problem of the Caputo-type fractional differential equation, and provide a basic for further research on the Caputo-type fractional differential equation and its applications. Other problems remain open for the location of the negative real zeros of the Mittag-Leffler functions used in this paper.