Robust stability problem in the mass-spring-damper system with general conformable fractional derivative

This paper considers a mass-spring-damper system that admits a external perturbation that is assumed to belong to a prefixed set of piecewise continuous functions. The general conformable fractional derivative is introduced in the second order differential equation that describes the dynamics of the mass-spring-damper system through the fractionalization method. The maximum deviation problem is formulated and studied in the resulting system of general conformable fractional differential equations. Using the solution of the maximum deviation problem, a maximum limit cycle is obtained, and this is used to establish a robust stability criterion for the solutions of the general conformable fractional differential equation. The robust stability criterion is obtained by considering an extension of the definition of stability under constant-acting perturbations that is used in systems of ordinary differential equations. The results obtained are illustrated numerically.