Mittag-Le­ffler stability for a one-dimensional fractional elastic-porous system: nonstandard frictional damping and nonstandard Kelvin-Voigt damping

Abstract

In this paper, we investigate the asymptotic behavior of solutions for a one-dimensional fractional elastic-porous system. We dissipate the system by two damping devices. The elastic equation is dissipated by a nonstandard frictional damping (frictional damping of fractional order) and the porous equation by a nonstandard Kelvin-Voigt damping (Kelvin-Voigt damping of fractional order). We prove that the system is Mittag-Leffler stable under certain conditions on the coefficients of the system and without imposing the equal wave speeds condition ρ/μ=J/δ. The result is new and opens the door for more research areas on porous-elastic systems and other problems.