This paper deals with a class of nonlinear Mathieu fractional differential equations. The reported results discuss the existence, uniqueness and stability for the solution of proposed equation. We prove the main results by the aid of fixed point theorems and Ulam’s approach. The paper is appended with two applications that describe the force of periodic pendulum and the motion of a particle in the plane. Graphical representations are used to illustrate the results.

中文翻译：

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Mathieu分数阶微分方程解的存在性和稳定性分析及其在某些物理现象上的应用

本文涉及一类非线性Mathieu分数阶微分方程。报道的结果讨论了所提出方程解的存在性，唯一性和稳定性。我们借助不动点定理和Ulam的方法证明了主要结果。本文附加了两个应用程序，描述了周期性摆的力和粒子在平面中的运动。图形表示用于说明结果。