Numerical schemes for initialized constant and variable fractional-order derivatives: matrix approach and its analog verification

DOI10.1177/1077546314565438zbMath1365.34135OpenAlexW1995641587MaRDI QIDQ5270807

Wiktor Malesza, Dominik Sierociuk, Michal Macias

Publication date: 3 July 2017

Published in: Journal of Vibration and Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1177/1077546314565438

zbMATH Keywords

fractional calculusfractional differential equationsinitial conditionsvariable-order systemsanalog model validation

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Functional-differential equations with fractional derivatives (34K37) Numerical methods for difference equations (65Q10)

Related Items (11)

King algorithm: a novel optimization approach based on variable-order fractional calculus with application in chaotic financial systems ⋮ Numerical solution of Caputo fractional differential equations with infinity memory effect at initial condition ⋮ Approximation methods for solving fractional equations ⋮ Non standard finite difference method for solving variable order fractional optimal control problems ⋮ The \(\psi\)-Hilfer fractional calculus of variable order and its applications ⋮ The Particular Types of Fractional Variable-Order Symmetric Operators ⋮ Realization of the Fractional Variable-Order Model with Symmetric Property ⋮ Approximate solutions for solving nonlinear variable-order fractional Riccati differential equations ⋮ Order Composition Properties for Output-Additive Variable-Order Derivative ⋮ Fractional-order value identification of the discrete integrator from a noised signal. I ⋮ Fractional variable-order derivative and difference operators and their applications to dynamical systems modelling

Cites Work

• Initial conditions and initialization of linear fractional differential equations
• Variable-order fractional derivatives and their numerical approximations
• How to impose physically coherent initial conditions to a fractional system?
• Fractional-order systems and controls. Fundamentals and applications
• Matrix approach to discrete fractional calculus. II: Partial fractional differential equations
• Variable order and distributed order fractional operators
• Modelling heat transfer in heterogeneous media using fractional calculus
• Matrix approach to discrete fractional calculus III: non-equidistant grids, variable step length and distributed orders
• Identification of Parameters of a Half-Order System

This page was built for publication: Numerical schemes for initialized constant and variable fractional-order derivatives: matrix approach and its analog verification