Semigroup property of fractional differential operators and its applications

Abstract

<p style='text-indent:20px;'>We establish partial semigroup property of families of Riemann-Liouville and Caputo fractional differential operators. Using this result we prove theorems on reduction of multi-term fractional differential systems to single-term and multi-order systems. As an application we obtain existence and uniqueness of solution to multi-term Caputo fractional differential systems.</p>