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1. On a Duffing-type oscillator differential equation on the transition to chaos with fractional q-derivatives.

Author

Houas, Mohamed, Samei, Mohammad Esmael, Sundar Santra, Shyam, and Alzabut, Jehad

Subjects
*DIFFERENTIAL equations, *NONLINEAR equations, *DUFFING equations, *FRACTIONAL calculus, *EQUATIONS
Abstract

In this paper, by applying fractional quantum calculus, we study a nonlinear Duffing-type equation with three sequential fractional q-derivatives. We prove the existence and uniqueness results by using standard fixed-point theorems (Banach and Schaefer fixed-point theorems). We also discuss the Ulam–Hyers and the Ulam–Hyers–Rassias stabilities of the mentioned Duffing problem. Finally, we present an illustrative example and nice application; a Duffing-type oscillator equation with regard to our outcomes. [ABSTRACT FROM AUTHOR]

Published
2024
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