Approximation and application of the Riesz-Caputo fractional derivative of variable order with fixed memory
Tomasz Błaszczyk, Krzysztof Bekus, Krzysztof Szajek, Wojciech Sumelka
Abstract
Abstract In this paper, the Riesz-Caputo fractional derivative of variable order with fixed memory is considered. The studied non-integer differential operator is approximated by means of modified basic rules of numerical integration. The three proposed methods are based on polynomial interpolation: piecewise constant, piecewise linear, and piecewise quadratic interpolation. The errors generated by the described methods and the experimental rate of convergence are reported. Finally, an application of the Riesz-Caputo fractional derivative of space-dependent order in continuum mechanics is depicted.
Topics & Concepts
MathematicsPiecewiseVariable (mathematics)Fractional calculusInterpolation (computer graphics)Applied mathematicsQuadratic equationPolynomialInteger (computer science)Rate of convergenceMathematical analysisOperator (biology)Constant (computer programming)Order (exchange)Convergence (economics)GeometryComputer scienceGeneProgramming languageRepressorFinanceAnimationBiochemistryTranscription factorComputer networkEconomic growthChannel (broadcasting)EconomicsComputer graphics (images)ChemistryFractional Differential Equations SolutionsComposite Structure Analysis and OptimizationNanofluid Flow and Heat Transfer