Novel Matrix-Based Methods for Fractional-Order Modeling

Abstract

Problem Area 1. Computational methods and numerical analysis for fractional differential equations. This is, in fact, the main goal of the proposed project. The work on various enhancements of the matrix approach, with the focus on using sparse matrices, parallel computations, grid computations, the Òshort- memory principleÓ, the Òmethod of large stepsÓ, etc.; all that including not only constant non-integer orders, but also variable and distributed orders. Problem Area 2. Fractional-order modeling of real-world systems. The other direction of the proposed research is fitting experimental data with the help of the Mittag-Leffler function; this can be called the ÒMittag-Leffler fittingÓ or the Òself-tuning fittingÓ. Problem Area 3. Experiments, demonstrations, software development. We will work with laboratory objects (e.g., some types of electrical circuits) for studying fractional-order behavior Òin situÓ and demonstrating applicability of our tools developed for data fitting and for numerical solution of fractional differential equations.

Document Details

Document Type
DoD Grant Award
Publication Date
Oct 30, 2018
Source ID
W911NF1510228

Entities

People

  • Igor Podlubny

Organizations

  • Army Contracting Command
  • Technical University of Košice
  • United States Army

Tags

Readers

  • Calculus or Mathematical Analysis
  • Parallel and Distributed Computing.
  • Wave Propagation and Nonlinear Chaotic Dynamics.