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Existence of smooth solutions of multi-term Caputo-type fractional differential equations (1705.02098v1)
Published 5 May 2017 in math.CA
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.