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

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

On a fractional problem of Lane-Emden type: Ulam type stabilities and numerical behaviors

In this work, we study some types of Ulam stability for a nonlinear fractional differential equation of Lane-Emden type with anti periodic conditions. Then, by using a numerical approach for the Caputo derivative, we investigate behaviors of the considered problem.WOS:0006715596000012-s2.0-8510973506