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

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.

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


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