Quasilinearization applied to boundary value problems at resonance for Riemann-Liouville fractional differential equations

Paul Eloe; Jaganmohan Jonnalagadda

doi:10.3934/dcdss.2020220

Article Contents

2020, Volume 13, Issue 10: 2719-2734. Doi: 10.3934/dcdss.2020220

This issue Previous Article Symmetries and conservation laws of a time dependent nonlinear reaction-convection-diffusion equation Next Article Exact and numerical solution of stochastic Burgers equations with variable coefficients

Quasilinearization applied to boundary value problems at resonance for Riemann-Liouville fractional differential equations

Paul Eloe^1, , and
Jaganmohan Jonnalagadda^2,

1.
Department of Mathematics, University of Dayton, Dayton, OH 45469-2316, USA
2.
Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad-500078, Telangana, India

^* Corresponding author: Paul Webster Eloe
^* Corresponding author: Paul Webster Eloe

Received: January 31, 2019

Revised: June 30, 2019

Early access: December 2019

Published: July 2020

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Abstract

The quasilinearization method is applied to a boundary value problem at resonance for a Riemann-Liouville fractional differential equation. Under suitable hypotheses, the method of upper and lower solutions is employed to establish uniqueness of solutions. A shift method, coupled with the method of upper and lower solutions, is applied to establish existence of solutions. The quasilinearization algorithm is then applied to obtain sequences of lower and upper solutions that converge monotonically and quadratically to the unique solution of the boundary value problem at resonance.

Keywords:

Boundary value problem at resonance,
Riemann-Liouville fractional differential equations,
upper and lower solutions,
quasilinearization.

Mathematics Subject Classification: Primary: 26A33, 34K10; Secondary: 34A45, 47H05, 65L10.

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