关键词: 单调迭代, 非线性分数阶微分方程, 比较原理, 极解

Abstract: By using the method of upper and lower solutions and the monotone iterative technique, we solved the initial value problem of a class of nonlinear fractional differential equations by establishing a new comparison principle, and obtained the result of the existence of extremal solutions of the initial problem.

Key words:  monotone iterative, comparison principle, extremal solution, nonlinear fractional differential equation