Generalized extension of the quasilinearization method for Riemann-Liouville fractional differential equations

Existence and comparison results of the linear and nonlinear Riemann-Liouville fractional differential equations of order q, 0 < q < 1, are recalled and modified where necessary. Using upper and lower solutions, an extension of the generalized quasilinearization method is developed for decomposed nonlinear fractional differential equations of order q containing generalized convex, concave, and nondifferentiable partitions. Quadratic convergence, and generalizations thereof, to the unique solution is proved via weighted sequences.