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

Autor:	Mohamed Houas, Mohammad Esmael Samei, Shyam Sundar Santra, Jehad Alzabut
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	Duffing differential equation Existence and uniqueness Fractional q-difference equations Ulam–Hyers stability Mathematics QA1-939
Zdroj:	Journal of Inequalities and Applications, Vol 2024, Iss 1, Pp 1-28 (2024)
Druh dokumentu:	article
ISSN:	1029-242X
DOI:	10.1186/s13660-024-03093-6
Popis:	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.
Databáze:	Directory of Open Access Journals
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