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Fractional Calculus and the Future of Science.

¹Center for Nonlinear Science, University of North Texas, Denton, TX 76203, USA.

Entropy (Basel, Switzerland)

|December 24, 2021

Summary

This anthology explores fractional calculus (FC), emphasizing the physical phenomena justifying fractional derivatives (FDs) before solving fractional differential equations. It bridges mathematical theory with real-world applications.

Area of Science:

Mathematics
Physics
Engineering

Background:

Fractional calculus (FC) offers advanced modeling capabilities beyond traditional integer-order derivatives.
Understanding the physical justification for employing fractional derivatives (FDs) is crucial for accurate scientific modeling.

Discussion:

This work examines the underlying physical phenomena that necessitate the use of FDs in mathematical models.
It explores the transition from integer-order to non-integer-order differentiation in describing complex systems.

Key Insights:

The anthology highlights the importance of physical interpretability when applying FC.
It provides a framework for selecting appropriate fractional orders based on observed phenomena.

Outlook:

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Future research will focus on developing novel methods for solving fractional differential equations.
The application of FC is expected to expand across various scientific disciplines.