Approximate Solutions of Nonlinear Pendulum with Fractional Damping

Because of many real problems are better characterized using fractional-order models, fractional calculus has recently become an intensively developing area of calculus not only among mathematicians but also among physicists and engineers as well. Fractional oscillator and fractional damped structure have attracted the attention of researchers in the field of mechanical and civil engineering [1-6]. This study is dedicated mainly a pendulum with fractional viscous damping. The mathematic model of pendulum is a cubic nonlinear equation governing the oscillations of systems having a single degree of freedom, via Riemann-Liouville fractional derivative. The method of multiple scales is performed to solve the equation by assigning the nonlinear and damping terms to the ε-order. Finally, the effects of the coefficient of a fractional damping term on the approximate solution are observed.