In this current paper, 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 point theorems. 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.
