A Dynamic-Order Fractional Dynamic System

TL;DR

This paper introduces dynamic-order fractional dynamic systems where the differential order depends on another system's output, providing insights into multi-system interactions and explaining complex physical phenomena.

Contribution

It presents the novel concept of dynamic-order fractional systems, linking system outputs to differential orders, and explores their properties and applications in physics.

Findings

Explains multi-system interactions through dynamic-order fractional systems

Analyzes anomalous relaxation and diffusion processes

Provides a new framework for physical mechanism understanding

Abstract

Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the differential-order of a fractional dynamic system is determined by the output signal of another dynamic system. The new concept offers a comprehensive explanation of physical mechanism of multi-system interaction. The properties and potential applications of dynamic-order fractional dynamic systems are further explored with the analysis of anomalous relaxation and diffusion processes.