Existence and Stability Analysis of Solution for Mathieu Fractional Differential Equations with Applications on Some Physical Phenomena

摘要

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.