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

Lan, Kunquan

doi:10.1090/proc/15169

Equivalence of higher order linear Riemann-Liouville fractional differential and integral equations
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Proc. Amer. Math. Soc. 148 (2020), 5225-5234 Request permission

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.

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