Comparative analysis of classical and fractional equations of motion

S. Sh. Rekhviashvili, A. V. Pskhu

Institute of Applied Mathematics and Automatization, Kabardino-Balkar Scientific Center, Russian Academy of Sciences, Nalchik, Russia

Abstract: The properties of dissipative systems, which are described by classical and fractional equations of motion, are analyzed. The Lagrange functions of these systems are presented and compared. Examples of infinitive and finite motion are considered. Based on the results obtained, a clarifying interpretation of fractional integro-differentiation in problems of mechanics is given.

Keywords: Lagrange equation, Lagrange function, equation of motion, energy dissipation, infinite and finite motions, fractional integro-differentiation.

Received: 14.12.2023
Revised: 14.12.2023
Accepted: 04.03.2024

DOI: 10.61011/PJTF.2024.11.57906.19845

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