Document Type
Article
Publication Date
2019
Publication Source
Electronic Journal of Differential Equations
Abstract
We apply the quasilinearization method to a Dirichlet boundary value problem and to a right focal boundary value problem for a RiemannLiouville fractional differential equation. First, we sue the method of upper and lower solutions to obtain the uniqueness of solutions of the Dirichlet boundary value problem. Next, we apply a suitable fixed point theorem to establish the existence of solutions. We develop a quasilinearization algorithm and construct sequences of approximate solutions that converge monotonically and quadratically to the unique solution of the boundary value problem. Two examples are exhibited to illustrate the main result for the Dirichlet boundary value problem.
ISBN/ISSN
1072-6691
Document Version
Published Version
Publisher
Texas State University
Volume
2019
Peer Reviewed
yes
Keywords
Riemann-Liouville fractional differential equation, Dirichlet boundary value problem; right focal boundary value problem, upper and lower solutions, quasilinearization
eCommons Citation
Eloe, Paul W. and Jonnalagadda, Jaganmohan, "Quasilinearization and Boundary Value Problems for Riemann-Liouville Fractional Differential Equations" (2019). Mathematics Faculty Publications. 211.
https://ecommons.udayton.edu/mth_fac_pub/211
Comments
This work is licensed under a Creative Commons Attribution 4.0 International License (CC-BY). This is an open-access journal, which means that all content is freely available without charges. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher.
It is article No. 58 in Volume 2019.