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

Author: Kunquan Lan
Journal: Proc. Amer. Math. Soc. 148 (2020), 5225-5234
MSC (2010): Primary 34A08; Secondary 26A33, 34A12, 45D05
DOI: https://doi.org/10.1090/proc/15169
Published electronically: September 18, 2020
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Abstract: A linear th order (Riemann-Liouville) fractional differential equation with initial values, together with a suitable assumption, is proved to be equivalent to a Volterra integral equation of the second kind involving an 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 th order fractional differential equation needs an additional condition to hold, and another strengthens a previous result on an th order fractional integral operator composed with an th order fractional differential operator.

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