#### FRACTIONAL DIFFERENTIAL EQUATION MODELING A VISCOELASTIC FLUID IN MASS-SPRING-MAGNETORHEOLOGICAL DAMPER MECHANICAL SYSTEM

###### Autor: Jesus Enrique Escalante Martínez

###### Coautor(es): J.E. Escalante-Martínez, L. J. Morales-Mendoza, C. Calderón-Ramón, J.R. Laguna-Camacho, I. Cruz-Orduña, E. Cardona Vargas

###### The mass-spring-damper system is the minimum complexity scenario that characterizes almost all the mechanical
vibration phenomena, it is well known that a second-order differential equation model its dynamics. However, if the
damper has a magnetorheological fluid in the presence of a magnetic field then the fluid shows viscoelastic properties.
Hence the mathematical model that best reflects the dynamics of this system is a fractional order differential equation.
Naturally, the Mittag-Leffler function appears as analytical solution. Accordingly we present here the mathematical
modeling of the mass-spring-magnetorheological damper system. The main result of our research is to show that the
viscous damping coefficient changes abruptly between two values approximately constant by tuning the magnetic
field strength, this was found when varying current intensity in the range of 0.2 to 2 Amperes. A Helmholtz coil is
used to produce the magnetic field.