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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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


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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Additional Information
  • Kunquan Lan
  • Affiliation: Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3 Canada
  • MR Author ID: 256493
  • Email:
  • Received by editor(s): March 3, 2020
  • Received by editor(s) in revised form: April 16, 2020
  • Published electronically: September 18, 2020
  • Additional Notes: The author was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada under grant no. 135752-2018.
  • Communicated by: Wenxian Shen
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 5225-5234
  • MSC (2010): Primary 34A08; Secondary 26A33, 34A12, 45D05
  • DOI:
  • MathSciNet review: 4163834