We apply the quasilinearization method to a Dirichlet boundary value problem and to a right focal boundary value problem for a Riemann-Liouville fractional Waste Receptacles 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 Jogger 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.