An efficient method for solving non-linear singularly perturbed two points boundary-value problems of fractional order

In this paper, we discuss a numerical solution of a class of non-linear fractional singularly perturbed two points boundary-value problem. The method of solution consists of solving reduced problem and boundary layer correction problem. A series method is used to solve the boundary layer correction problem, and then the series solutions is approximated by the Pade’ approximant of order [m, m]. Some theoretical results are established and proved. Two numerical examples are discussed to illustrate the efficiency of the present scheme.

► We discuss a non-linear singularly perturbed two points boundary-value problem of fractional order.
► We prove the maximum principle theorem for the present problem.
► We address the uniform stability of the solution of the problem.
► We prove the uniqueness of the solution of the problem.
► We solve the present problem using reduced and boundary layer correction method.