The role of α-inequalities in examining the singular version of the Big Bang model

Authors

SAMANE IJADIFollow
S. MANSOUR VAEZPOURFollow
MEHDI SHABIBIFollow
SHAHRAM REZAPOURFollow

Author ORCID Identifier

SAMANE IJADI: 0009-0006-0649-0057

S. MANSOUR VAEZPOUR: 0000-0003-3909-4203

MEHDI SHABIBI: 0000-0001-7380-1595

SHAHRAM REZAPOUR: 0000-0003-3463-2607

Abstract

In this article, by extending Friedmann's equation, we propose a singular fractional differential system for the Big Bang model. In this model, the rate of increase in the size of the universe tends to infinity at time near to zero and causes the emergence of a singular differential equation,which physically justifies the near-infinity energy of the universe in the near-zero volume of the universe in the early moments of the Big Bang. Then, we investigate this type of strong singular boundary value problem, by using $\alpha$-inequalities. In the sequel, some examples, describe the main results. Moreover, we present numerical and graphical simulations to illustrate the convergence of solutions for this singular problem.

DOI

10.55730/1300-0098.3570

Keywords

α-inequalities, Big Bang, Caputo derivative, convert singular, fractional calculus, singularity

First Page

1

Last Page

17

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

IJADI, SAMANE; VAEZPOUR, S. MANSOUR; SHABIBI, MEHDI; and REZAPOUR, SHAHRAM (2025) "The role of α-inequalities in examining the singular version of the Big Bang model," Turkish Journal of Mathematics: Vol. 49: No. 1, Article 2. https://doi.org/10.55730/1300-0098.3570
Available at: https://journals.tubitak.gov.tr/math/vol49/iss1/2