Equivalence of higher order linear Riemann-Liouville fractional differential and integral equations

Abstract

A linear $n$th order (Riemann-Liouville) fractional differential equation with $m+1$ initial values, together with a suitable assumption, is proved to be equivalent to a Volterra integral equation of the second kind involving an $n$th order (Riemann-Liouville) fractional integral operator. Two special cases of the result are given: one shows that a well-known result on the solution of an $n$th order fractional differential equation needs an additional condition to hold, and another strengthens a previous result on an $n$th order fractional integral operator composed with an $n$th order fractional differential operator.

Topics & Concepts