Electron. J. Differential Equations,
Vol. 2019 (2019), No. 58, pp. 115.
Quasilinearization and boundary value problems for RiemannLiouville
fractional differential equations
Paul W. Eloe, Jaganmohan Jonnalagadda
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.
Submitted August 14, 2018. Published May 3, 2019.
Math Subject Classifications: 26A33, 34K10, 34A45, 47H05.
Key Words: RiemannLiouville fractional differential equation;
Dirichlet boundary value problem; right focal boundary value problem;
upper and lower solutions, quasilinearization.
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Paul W. Eloe
Department of Mathematics
University of Dayton
Dayton, OH 454692316, USA
email: peloe1@udayton.edu


Jaganmohan Jonnalagadda
Department of Mathematics
Birla Institute of Technology and Science Pilani
Hyderabad500078, Telangana, India
email: j.jaganmohan@hotmail.com

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