Connection of Mechanics and Fractional Derivatives

Abstract:

The concept of fractional derivative as a mathematical operation was first proposed by Leibniz.In recent years, it has appeared increasingly in constitutive equations that describe the behavior ofvarious materials. This naturally raises the question of whether fractional differentiation could haveimplications for the fundamental structure of Newtonian mechanics. In this study, this possibility isinvestigated in the context of the mechanics of a system of material points. The analysis is grounded inthe principle of stationary action, which, following the seminal works of Noether, serves as a unifyingfoundation across the various branches of physics. This principle provides a coherent framework thatencompasses the established variables and theorems, enabling the derivation of general conclusions.Accordingly, it offers a suitable theoretical basis for examining the role of fractional derivatives withinmechanical systems.

• Periodical: Advances in Science and Technology (Volume 181)
• Pages: 29-37
• DOI: https://doi.org/10.4028/p-Yg97RQ
• Online since: August 2026
• Authors: Peter B. Béda*, Gyula Béda
• Keywords: Fractional Calculus, Lagrange Function, Variational Principles

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