Formulation and solutions of fractional continuously variable order mass spring damper systems controlled by viscoelastic and viscous-viscoelastic dampers

摘要

The article presents the formulation and a new approach to find analyticsolutions for fractional continuously variable order dynamic models viz.Fractional continuously variable order mass-spring damper systems. Here, we usethe viscoelastic and viscous-viscoelastic dampers for describing the dampingnature of the oscillating systems, where the order of fractional derivativevaries continuously. Here, we handle the continuous changing nature offractional order derivative for dynamic systems, which has not been studiedyet. By successive iteration method, here we find the solution of fractionalcontinuously variable order mass-spring damper systems, and then give a closeform solution. We then present and discuss the solutions obtained in the caseswith continuously variable order of damping for this oscillator with graphicalplots.