Title: Existence of smooth solutions of multi-term Caputo-type fractional differential equations,
Abstract: This paper deals with the initial value problem for the multi-term fractional
differential equation. The fractional derivative is defined in the Caputo
sense. Firstly the initial value problem is transformed into a equivalent
Volterra-type integral equation under appropriate assumptions. Then new
existence results for smooth solutions are established by using the Schauder
fixed point theorem.