变分数阶非局部边值问题的再生核配置法

Reproducing Kernel Collocation Method for Variable Fractional Nonlocal Boundary Value Problems

变分数阶微分方程在很多领域具有重要的应用.本文拟提出求解变分数阶非局部边值问题的再生核配置法,该方法结合了分段多项式再生核和多项式再生核的优点,而且可以避免满足线性非局部边界条件的核函数的构造.通过数值算例与已存在的方法进行比较,数值结果表明该方法是有效的.

Variable fractional differential equations have important applications in many fields.In this paper,our goal is to present a new reproducing kernel collocation method for solving nonlocal variable fractional boundary value problems.The method combinesthe advantages of the reproducing kernel basis function and thepolynomial basis function.The present method can avoid finding a reproducing kernel satisfying nonlocal boundary conditions.Numerical experiments are carried out to demonstrate the validity of the new technique compared with the existing methods.