@misc{10481/90540,
year = {2024},
url = {https://hdl.handle.net/10481/90540},
abstract = {This study investigates the interconnections between the traditional Fokker-Planck Equation (FPE) and its
fractal counterpart (FFPE), utilizing fractal derivatives. By examining the continuous approximation of fractal
derivatives in the FPE, it derives the Plastino-Plastino Equation (PPE), which is commonly associated with Tsallis
Statistics. This work deduces the connections between the entropic index and the geometric quantities related to
the fractal dimension. Furthermore, it analyzes the implications of these relationships on the dynamics of systems
in fractal spaces. To assess the effectiveness of both equations, numerical solutions are compared within the
context of complex systems dynamics, specifically examining the behaviours of quark-gluon plasma (QGP). The
FFPE provides an appropriate description of the dynamics of fractal systems by accounting for the fractal nature
of the momentum space, exhibiting distinct behaviours compared to the traditional FPE due to the system’s
fractal nature. The findings indicate that the fractal equation and its continuous approximation yield similar
results in studying dynamics, thereby allowing for interchangeability based on the specific problem at hand.},
organization = {Project INCT-FNA (Instituto Nacional de
Ciência e Tecnologia - Física Nuclear Aplicada) Proc. No. 464898/2014-
5},
organization = {Conselho Nacional de Desenvolvimento Científico e Tecnológico
(CNPq-Brazil), grant 306093/2022-7},
organization = {Project INCT-FNA
Proc. No. 464 898/2014-5},
organization = {FAPESP, Brazil grant 2016/17612-7},
organization = {Project PID2020-114767GB-I00
funded by MCIN/AEI/10.13039/501100011033},
organization = {FEDER/Junta
de Andalucía-Consejería de Economía y Conocimiento 2014-2020 Operational
Program under Grant A-FQM178-UGR18},
organization = {Junta de
Andalucía under Grant FQM-225},
organization = {Ramón y Cajal Program of the Spanish MICIN and by the European
Social Fund under Grant RYC-2016-20678},
organization = {“Prórrogas
de Contratos Ramón y Cajal” Program of the University of Granada},
publisher = {Elsevier},
title = {Dynamics in fractal spaces},
doi = {10.1016/j.physletb.2023.138370},
author = {Megías Fernández, Eugenio and Golmankhaneh, Alireza Khalili and Deppman, Airton},
}