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Using the Hilfer–Katugampola fractional derivative in initial-value Mathieu fractional differential equations with application to a particle in the plane

Amel Berhail, Nora Tabouche, Jehad Alzabut, Mohammad Esmael Samei

2022Advances in Continuous and Discrete Models19 citationsDOIOpen Access PDF

Abstract

Abstract We examine a class of nonlinear fractional Mathieu equations with a damping term. The equation is an important equation of mathematical physics as it has many applications in various fields of the physical sciences. By utilizing Schauder’s fixed-point theorem, the existence arises of solutions for the proposed equation with the Hilfer–Katugampola fractional derivative, and an application is additionally examined. Two examples guarantee the obtained results.

Topics & Concepts

Fractional calculusMathieu functionFixed-point theoremMathematicsNonlinear systemMathematical analysisSchauder fixed point theoremDifferential equationApplied mathematicsPhysicsPicard–Lindelöf theoremQuantum mechanicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisAdvanced Differential Equations and Dynamical Systems
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