Communications on Applied Nonlinear Analysis
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.
boundary value problem at resonance, Caputo fractional differential equations, shift method, upper and lower solutions, quasilinearization.
Almuthaybiri, Saleh S.; Eloe, Paul W.; and Neugebauer, Jeffrey T., "Quasilinearization and Boundary Value Problems at Resonance for Caputo Fractional Differential Equations" (2019). Mathematics Faculty Publications. 206.