2011/11/08 by Thomas M. Michelitsch, Thomas Michelitsch, Gérard A. Maugin +10
Engineering · Physics and Astronomy · #Classical Physics (physics.class-ph) #Elasticity and Material Modeling #Elasticity and Wave Propagation #FOS: Physical sciences #Thermoelastic and Magnetoelastic Phenomena #physics.class-ph
paper · pdf · doi:10.48550/arxiv.1111.1898
arxiv created 2011/11/08 · openalex publication_date 2011/11/08 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this communication is to propose a generalized notion of the "traditional derivative". This generalization includes the fractional derivatives such as the Riemann-Liouville, Gruenwald-Letnikov, Weyl, Riesz, Caputo, Marchaud derivatives and other variants as special cases. The approach is useful to describe mechanical problems in material systems with microstructures without characteristic scale such as self-similar and fractal materials.