On a Duffing-type oscillator differential equation on the transition to chaos with fractional q-derivatives
Mohamed Houas, Mohammad Esmael Samei, Shyam Sundar Santra, Jehad Alzabut
Abstract
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.
Topics & Concepts
MathematicsDuffing equationType (biology)Differential equationMathematical analysisCHAOS (operating system)Differential (mechanical device)Pure mathematicsMathematical physicsNonlinear systemQuantum mechanicsPhysicsThermodynamicsComputer scienceEcologyComputer securityBiologyFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisFunctional Equations Stability Results