Existence and stability of solutions for linear and nonlinear damping of q−fractional Duffing-Rayleigh problem

In this current paper, by using q−fractional calculus, we study the Duffing-Rayleigh type problem with sequential fractional q−derivative of the Caputo type. We investigate the existence and uniqueness of solutions by applying some classical fixed pointtheorems. Also we define and study the Ulam-Hyers and the Ulam-Hyers-Rassias stabilities of solutions for our problem. An example is presented to illustrate the main results.(2010) Mathematics Subject Classifications: 26A33, 39B72, 34C45.