New Van der Pol–Duffing Jerk Fractional Differential Oscillator of Sequential Type

Abstract

The subject of this paper is the existence, uniqueness and stability of solutions for a new sequential Van der Pol–Duffing (VdPD) jerk fractional differential oscillator with Caputo–Hadamard derivatives. The arguments are based upon the Banach contraction principle, Krasnoselskii fixed-point theorem and Ulam–Hyers stabilities. As applications, one illustrative example is included to show the applicability of our results.

Keywords

• Van der Pol–Duffing jerk equation
• fixed point
• uniqueness
• Caputo–Hadamard fractional derivative
• Ulam–Hyers stability