Fractional Time-Delayed differential equations: Applications in Cosmological Studies
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Micolta-Riascos, Bayron Droguett, Byron Marriaga, Gisel Mattar Leon, Genly Paliathanasis, Andronikos del Campo, Luis Leyva, Yoelsy |
| author_facet | Micolta-Riascos, Bayron Droguett, Byron Marriaga, Gisel Mattar Leon, Genly Paliathanasis, Andronikos del Campo, Luis Leyva, Yoelsy |
| contents | Fractional differential equations model processes with memory effects, providing a realistic perspective on complex systems. We examine time-delayed differential equations, discussing first-order and fractional Caputo time-delayed differential equations. We derive their characteristic equations and solve them using the Laplace transform. We derive a modified evolution equation for the Hubble parameter incorporating a viscosity term modeled as a function of the delayed Hubble parameter within Eckart's theory. We extend this equation using the last-step method of fractional calculus, resulting in Caputo's time-delayed fractional differential equation. This equation accounts for the finite response times of cosmic fluids, resulting in a comprehensive model of the Universe's behavior. We then solve this equation analytically. Due to the complexity of the analytical solution, we also provide a numerical representation. Our solution reaches the de Sitter equilibrium point. Additionally, we present some generalizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05705 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Time-Delayed differential equations: Applications in Cosmological Studies Micolta-Riascos, Bayron Droguett, Byron Marriaga, Gisel Mattar Leon, Genly Paliathanasis, Andronikos del Campo, Luis Leyva, Yoelsy General Relativity and Quantum Cosmology Mathematical Physics Fractional differential equations model processes with memory effects, providing a realistic perspective on complex systems. We examine time-delayed differential equations, discussing first-order and fractional Caputo time-delayed differential equations. We derive their characteristic equations and solve them using the Laplace transform. We derive a modified evolution equation for the Hubble parameter incorporating a viscosity term modeled as a function of the delayed Hubble parameter within Eckart's theory. We extend this equation using the last-step method of fractional calculus, resulting in Caputo's time-delayed fractional differential equation. This equation accounts for the finite response times of cosmic fluids, resulting in a comprehensive model of the Universe's behavior. We then solve this equation analytically. Due to the complexity of the analytical solution, we also provide a numerical representation. Our solution reaches the de Sitter equilibrium point. Additionally, we present some generalizations. |
| title | Fractional Time-Delayed differential equations: Applications in Cosmological Studies |
| topic | General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2504.05705 |