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
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