Solving fractional two-point boundary value problems using continuous analytic method

In this article, the homotopy analysis method is applied to provide approximate solutions for linear and nonlinear two-point boundary value problems of fractional order. The solution was calculated in the form of a convergent power series with easily computable components. In this method, one has great freedom to select auxiliary functions, operators, and parameters in order to ensure the convergence of the approximate solution and to increase both the rate and region of convergence. Numerical examples are provided to demonstrate the accuracy and efficiency of the present method. Meanwhile, further iterations can produce more accurate results and decrease the error.