2008/08/01 by Pierre Inizan · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Thermoelastic and Magnetoelastic Phenomena #math-ph #math.DS #math.MP
paper · pdf · doi:10.1063/1.2963497
published as Journal of Mathematical Physics 49, 8 (2008) 082901 · 14 pages
openalex publication_date 2008/08/01 · arxiv created 2008/08/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fractional equations appear in the description of the dynamics of various physical systems. For Lagrangian systems, the embedding theory developed by Cresson [“Fractional embedding of differential operators and Lagrangian systems,” J. Math. Phys. 48, 033504 (2007)] provides a univocal way to obtain such equations, stemming from a least action principle. However, no matter how equations are obtained, the dimension of the fractional derivative differs from the classical one and may induce problems of temporal homogeneity in fractional objects. In this paper, we show that it is necessary to introduce an extrinsic constant of time. Then, we use it to construct two equivalent fractional embeddings which retains homogeneity. The notion of fractional constant is also discussed through this formalism. Finally, an illustration is given with natural Lagrangian systems, and the case of the harmonic oscillator is entirely treated.