Translator Disclaimer
October 2021 A note on generalized Abel equations with constant coefficients
Yulong Li
Rocky Mountain J. Math. 51(5): 1749-1760 (October 2021). DOI: 10.1216/rmj.2021.51.1749

Abstract

The generalized Abel equation (GAE) with constant coefficients, γ1aDxσu+γ2xDbσu=f, 0<σ<1, has renewed interest since it has appeared as a component in double-sided fractional diffusion equations. Motivated by direct applications in modeling, we seek the necessary and sufficient conditions for interchanging the order of differentiation and fractional integration in GAEs. Put another way, assume functions u,v,f lie in Hölder spaces that admit integrable singularities at the endpoints and

γ1aDxσu+γ2xDbσu=f andγ1aDxσv+γ2xDbσv=Df,

then we prove that Du=v if and only if u(a)=u(b)=0.

Citation

Download Citation

Yulong Li. "A note on generalized Abel equations with constant coefficients." Rocky Mountain J. Math. 51 (5) 1749 - 1760, October 2021. https://doi.org/10.1216/rmj.2021.51.1749

Information

Received: 30 January 2021; Revised: 11 March 2021; Accepted: 14 March 2021; Published: October 2021
First available in Project Euclid: 17 February 2022

Digital Object Identifier: 10.1216/rmj.2021.51.1749

Subjects:
Primary: 45E10
Secondary: 45B99

Keywords: Abel , homogeneous boundary , integral equation

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
12 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.51 • No. 5 • October 2021
Back to Top