FRACTIONAL CALCULUS AND DYNAMICAL SYSTEMS
Fractional calculus has come to prominence relatively recently, even though it has been formally available since the mid 19th century. Beginning with applications in the modeling of viscoelastic materials in the 1960s, fractional dynamical systems have yielded a modeling approach that provides another parameter that may be tuned to better fit data. Our group has developed system identification methods and DMD modeling techniques for fractional order dynamical systems as well as numerical techniques and new reproducing kernel Hilbert spaces intertwining multiplication operators with the Caputo fractional derivative via adjoint relations.
Numerical Methods
Convergence Rate Estimates for the Kernelized Adams Bashforth Moulton Method for Fractional Order Initial Value Problems
Joel A. Rosenfeld and Warren E. Dixon
(Accepted at Fractional Calculus and Applied Analysis)
A Mesh-free Pseudospectral Approachfor Estimating the Fractional Laplacian via Radial Basis Functions
Joel A. Rosenfeld, Spencer A. Rosenfeld, Warren E. Dixon
Approximating the Caputo Fractional Derivative throughthe Mittag-Leffler Reproducing Kernel Hilbert Space and the Kernelized Adams-Bashforth-Moulton Method,
Joel A. Rosenfeld and Warren E. Dixon
System Identification
Fractional Order System Identification with Occupation KernelRegression
Xiuying Li and Joel A. Rosenfeld
(Under Review)
Hilbert Spaces and Operator Theory
Mittag-Leffler Reproducing Kernel Hilbert Spaces of Entire and Analytic Function
Joel A. Rosenfeld, Benjamin P. Russo, Warren E. Dixon