Generalized quasilinearization method for RL fractional differential equations

Abstract

Existence and comparison results of the linear and nonlinear Riemann-Liouville fractional differential equations and nonlinear systems of order q, 0 < q < 1, are recalled and modified where necessary. Generalized quasilinearization method is developed for decomposed nonlinear fractional differential equations of order q, using coupled upper and lower solutions. Quadratic convergence to the unique solution is proved via weighted sequences.