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

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.

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.

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