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
MathSciNet review:
4163834
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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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Additional Information
Kunquan Lan
Affiliation:
Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3 Canada
MR Author ID:
256493
Email:
klan@ryerson.ca
Keywords:
Riemann-Liouville fractional integral operator,
Riemann-Liouville fractional differential operator,
linear fractional differential equation,
Volterra integral equation of the second kind,
initial value problems,
equivalence
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
Article copyright:
© Copyright 2020
American Mathematical Society