A Computational Approach to Exponential-Type Variable-Order Fractional Differential Equations
Roberto Garrappa, Andrea Giusti
Abstract
Abstract We investigate the properties of some recently developed variable-order differential operators involving order transition functions of exponential type. Since the characterization of such operators is performed in the Laplace domain, it is necessary to resort to accurate numerical methods to derive the corresponding behaviours in the time domain. In this regard, we develop a computational procedure to solve variable-order fractional differential equations of this novel class. Furthermore, we provide some numerical experiments to show the effectiveness of the proposed technique.
Topics & Concepts
MathematicsLaplace transformVariable (mathematics)Domain (mathematical analysis)Exponential functionType (biology)Applied mathematicsDifferential equationOrder (exchange)Exponential typeClass (philosophy)Mathematical analysisComputer scienceBiologyArtificial intelligenceEconomicsEcologyFinanceFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsNonlinear Differential Equations Analysis