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

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 Ula...

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Bibliographic Details
Published in:Journal of inequalities and applications 2024-01, Vol.2024 (1), p.12-28, Article 12
Main Authors: Houas, Mohamed, Samei, Mohammad Esmael, Sundar Santra, Shyam, Alzabut, Jehad
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Calculus
Derivatives
Differential equations
Duffing differential equation
Existence and uniqueness
Existence theorems
Fixed points (mathematics)
Fractional q-difference equations
Mathematics
Mathematics and Statistics
Ordinary differential equations
Oscillators
Partial differential equations
Ulam–Hyers stability
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Summary: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.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-024-03093-6