2015/08/21 by S. Saha Ray, S. Sahoo, Ray, S. Saha +3
Engineering · Mathematics · #Advanced Control Systems Design #Classical Physics (physics.class-ph) #FOS: Physical sciences #Fractional Differential Equations Solutions #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1508.06202
openalex publication_date 2015/08/21 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
The article presents the formulation and a new approach to find analytic\nsolutions for fractional continuously variable order dynamic models viz.\nFractional continuously variable order mass-spring damper systems. Here, we use\nthe viscoelastic and viscous-viscoelastic dampers for describing the damping\nnature of the oscillating systems, where the order of fractional derivative\nvaries continuously. Here, we handle the continuous changing nature of\nfractional order derivative for dynamic systems, which has not been studied\nyet. By successive iteration method, here we find the solution of fractional\ncontinuously variable order mass-spring damper systems, and then give a close\nform solution. We then present and discuss the solutions obtained in the cases\nwith continuously variable order of damping for this oscillator with graphical\nplots.\n