https://doi.org/10.1140/epjp/s13360-025-06389-8
Regular Article
Self-gravitating anisotropic spheres and non-local equations of state through the fractional calculus
1
Departamento de Física Aplicada, Universidad de Alicante, Campus de San Vicente del Raspeig, 03690, Alicante, Spain
2
Departamento de Matemáticas, Colegio de Ciencias e Ingeniería, Universidad San Francisco de Quito, 170901, Quito, Ecuador
3
Departamento de Física, Facultad de Ciencias Naturales y Matemáticas, Escuela Superior Politécnica del Litoral, P.O. Box 09-01-5863, Guayaquil, Ecuador
4
Institute for Theoretical Physics, University of Regensburg, 93040, Regensburg, Germany
Received:
15
April
2025
Accepted:
28
April
2025
Published online:
28
May
2025
In this work, we study static, spherically symmetric anisotropic configurations that obey a non-local equation of state relating radial pressure and energy density. Non-locality is introduced via the Caputo fractional derivative. We analyze in detail the impact of the fractional parameter on the behavior of the material sector. We find that for some values of the parameter, the mass density, the radial and tangential pressures reach their maximum value at the center and decrease monotonically toward the surface, as expected. We analyze the maximum mass allowed by our solution thorough a M-R diagram. We find that, based on the parameters considered, the maximum mass is on the order of three solar masses for a radius of approximately 15.6 km. We also find that increasing the fractional parameter leads to an increase in the compactness of the star, from 0.19 to 0.28.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
