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

Ain Shams Engineering Journal

Ahmad El-Ajou¹  Omar Abu Arqub¹  Shaher Momani² 

[1] Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan;Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan;

关键词: Homotopy analysis method;    Fractional boundary value problem;    Caputo derivative;   

DOI  :  10.1016/j.asej.2012.11.010

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown