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

Amira Abdelnebi () and Zoubir Dahmani
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Amira Abdelnebi: Laboratory LPAM, UMAB, University of Mostaganem, Mostaganem 27000, Algeria
Zoubir Dahmani: Laboratory LPAM, UMAB, University of Mostaganem, Mostaganem 27000, Algeria

Mathematics, 2022, vol. 10, issue 19, 1-16

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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