A novel approach to study the mass-spring-damper system using a reliable fractional method

This paper proposes some modifications to the method of studying the fractional mass-spring-damper system in order to meet the high reliability requirements of the mechanical system. These changes mainly depend on two things, the discovered drawback of the fractional methods, and the general behavior of the mechanical damping system. The defects discovered in fractional calculus are summarized in the results of differences between the variance of fractional definitions and the constant coefficients. Therefore, it became necessary to introduce some modifications and suggestions for compatibility with the system to make the proposed fractional definition more intuitive and usable. In this paper, the numerical and theoretical results were compared using our proposed definition and Caputo’s. We found that there is a clear difference in the results between them. We believe that our proposed method distinguished by its compatibility with the basics of damped mechanical system behavior. In first method the vibration takes place around the reference axis, while in Caputo’s method vibration occurs around different axes when changing the fractional differential orders. The method proposed is based on a modification in conformable fractional derivative.