Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 58, pp. 1-15.

Title: Quasilinearization and boundary value problems for Riemann-Liouville
       fractional differential equations

Authors: 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
 Riemann-Liouville 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 03, 2019.
Math Subject Classifications: 26A33, 34K10, 34A45, 47H05.
Key Words: Riemann-Liouville fractional differential equation;
           Dirichlet boundary value problem; right focal boundary value problem;
           upper and lower solutions, quasilinearization.