关键词: 分数阶微分方程, 边值问题, 增算子不动点定理, 上下解, 极解

Abstract:

We considered a class of nonlinear fractional differential equations with integral terms, and the corresponding Green’s function of equations was obtained by computing. We used the increasing operator fixed point theorem and the method of upper and lower solutions to prove the existence and uniqueness of extremal solutions of the equation, and gave the display iterative format of the approximate extremal solutions.

Key words: fractional differential equation, boundary value problem, increasing operator fixed point theorem, upper and lower solution, extremal solution