Document Type
Article
Publication Date
2019
Publication Source
Communications on Applied Nonlinear Analysis
Abstract
The quasilinearization method is applied to a boundary value problem at resonance for a Caputo fractional differential equation. The method of upper and lower solutions is first employed to obtain the uniqueness of solutions of the boundary value problem at resonance. The shift argument is applied to show the existence of solutions. The quasilinearization algorithm is then developed and sequences of approximate solutions are constructed that converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two applications are provided to illustrate the main results.
Inclusive pages
80-100
ISBN/ISSN
1074-133X
Document Version
Postprint
Publisher
International Publications
Volume
26
Issue
3
Peer Reviewed
yes
Keywords
boundary value problem at resonance, Caputo fractional differential equations, shift method, upper and lower solutions, quasilinearization.
eCommons Citation
Almuthaybiri, Saleh S.; Eloe, Paul W.; and Neugebauer, Jeffrey T., "Quasilinearization and Boundary Value Problems at Resonance for Caputo Fractional Differential Equations" (2019). Mathematics Faculty Publications. 206.
https://ecommons.udayton.edu/mth_fac_pub/206
COinS
Comments
The accepted manuscript of this article is made available with the permission of the author; the publisher's self-archiving policy is unknown. Permission is pending; request documentation is on file.