Semigroup property of fractional differential operators and its applications

TL;DR

This paper investigates the semigroup property of fractional differential operators and applies it to simplify multi-term fractional systems, establishing existence and uniqueness of solutions.

Contribution

It introduces a partial semigroup property for Riemann-Liouville and Caputo operators and uses it to reduce complex systems to simpler forms with proven solution properties.

Findings

Partial semigroup property established for fractional operators

Reduction of multi-term systems to single-term systems

Existence and uniqueness of solutions proven

Abstract

We establish partial semigroup property 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, and prove existence and uniqueness of solution to multi-term Caputo fractional differential systems