This work 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 an equivalent Volterra-type integral equation under appropriate assumptions. Then, new existence results for smooth solutions are established by using the Schauder fixed point theorem.
Digital Object Identifier (DOI)
Sin, Chung-Sik; Ri, Gang-Il; and Kim, Mun-Chol
"Existence of Smooth Solutions of Multi-Term Caputo-Type Fractional Differential Equations,"
Progress in Fractional Differentiation & Applications: Vol. 4
, Article 5.
Available at: https://dc.naturalspublishing.com/pfda/vol4/iss3/5