An approach for the approximate solution of the fractional Troesch’s problem

We use the Green’s function and Picard’s fixed point iteration to introduce a new semi-analytical iterative method for the approximate solution of the nonlinear fractional Troesch’s boundary-value problem. Moreover, we establish the convergence of our scheme for small values of the eigenvalues. Finally, various numerical experiments are presented to demonstrate that our method handles efficiently the boundary layer, cuts down on the time-consuming calculation, offers quick convergence, and produces accurate results. To our best knowledge, this is the first attempt to extend the traditional Troesch’s problem to the fractional case.