Review of Some Promising Fractional Physical Models

TL;DR

This paper reviews promising fractional physical models that utilize fractional calculus to describe systems with non-locality, memory, and fractal properties, highlighting their potential for future research in physics and mechanics.

Contribution

It provides an overview of fractional calculus applications in physics, introducing models of systems with memory, long-range interactions, and fractal media, including quantum and nano-system analogs.

Findings

Models of discrete systems with memory are discussed.

Applications in fractal media dynamics are presented.

Quantum and nano-system models with fractional derivatives are explored.

Abstract

Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and differentiation of non-integer orders, i.e., by methods of the fractional calculus. This paper is a review of physical models that look very promising for future development of fractional dynamics. We suggest a short introduction to fractional calculus as a theory of integration and differentiation of non-integer order. Some applications of integro-differentiations of fractional orders in physics are discussed. Models of discrete systems with memory, lattice with long-range inter-particle interaction, dynamics of fractal media are presented. Quantum analogs of fractional derivatives and model of open nano-system systems with memory are also discussed.