@article{Rubio-López2026, 
author = {Franco Rubio-López and Dennis Quispe-Sánchez and Obidio Rubio},
title = {Geometric interpretation of Caputo's fractional derivative and its relation to initial value problems of integer and fractional order},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {10831-10856},
keywords = {curvature of curve, fractional curvature, Caputo's fractional derivative, geometric interpretation, Frenet-Serret equations},
url = {https://www.sciopen.com/article/10.3934/math.2026445},
doi = {10.3934/math.2026445},
abstract = {In this paper, we give a new geometric interpretation to Caputo's fractional derivative, based on the fundamental theorem of plane curves and the fractional curvature of plane curves introduced by Rubio-López et al. in 2023. Furthermore, our results are related to initial value problems of integer and fractional order. Finally, some examples related to differential geometry and viscoelasticity theory are given.}
}