变分法研究一类分数阶微分方程边值问题解的存在性

The variational method is used to study the existence of solutions to boundary value problems for a class of fractional differential equations

摘要: 利用一类分数阶微分方程边值问题的变分法, 建立了该边值问题解存在的充分条件. 然后将问题归结为一个等价的积分形式, 使得边值问题的解被定义为对应泛函的临界点. 最后利用山路引理，建立了该边值问题解的存在性.

Abstract: A sufficient condition for the existence of the solution of a boundary value problem for a class of fractional-order differential equations is established by using the variational method. Then the problem is reduced to an equivalent integral form so that the solution of the boundary value problem is defined as the critical point of the corresponding functional. Finally, the existence of the solution to the boundary value problem is established by using the mountain road lemma.