A Cosmology Governed by a Fractional Differential Equation and the Generalized Kilbas-Saigo-Mittag-Leffler Function

El-Nabulsi, Rami Ahmad

doi:10.1007/s10773-015-2700-5

Cited by 30 publications

(19 citation statements)

References 58 publications

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“…In Refs. [93,94], the FRW cosmology characterized by a scale factor obeying different independent types of fractional differential equations was studied, and both types of fractional operators: the Riemann-Liouville fractional integral and the Caputo fractional derivative were considered. The solutions for such models are given in terms of Mittag-Leffler and generalized Kilbas-Saigo-Mittag-Leffler functions.…”

Section: Some Recent Studies Of Facmentioning

confidence: 99%

Fractional-order derivatives in cosmological models of accelerated expansion

Shchigolev

2021

Preprint

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In this brief review, we present the results of the fractional differential approach in cosmology in the context of the exact models of cosmological accelerated expansion obtained by several authors to date. Most of these studies are devoted to the problem of introducing fractional derivatives or fractional integrals into the classical General Relativity (GR). There are several observational and theoretical motivations to investigate the modified or alternative theories of GR. Among other things, we cover General Relativity modified by a phenomenological approach dealing with fractional calculus. At the same time, a sufficiently large number of exact solutions of the cosmological equations modified by this approach were obtained. Some of these models may be especially relevant in the light of solving the problem of late accelerated expansion of the universe. These studies are largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.

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Section: Some Recent Studies Of Facmentioning

confidence: 99%

Fractional-order derivatives in cosmological models of accelerated expansion

Shchigolev

2021

Preprint

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“…Among the many applications, this multi-fractional scenario has provided some insights on the relevant particle physics and cosmology issues [6][7][8][9]. Although these investigations mostly focus on the theory T q and theory T v , one may find diverse approaches to the cosmology with fractional derivatives in [10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Hawking radiation of a multi-fractional Schwarzschild black hole

Huang¹,

Yuan²

2020

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Following the initial work of Calcagni et al. on the black holes in multi-fractional theories, we focus on the Schwarzschild black hole in multi-fractional theory with q-derivatives. After presenting its Hawking and Hayward temperatures in detail, we verify these results by appealing to the wellknown Hamilton-Jacobi and null geodesic methods of the tunnelling approach to Hawking radiation.A special emphasis is placed on the difference between the geometric and fractional frames.

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“…Fractional differential equations (FDE) become an important tool in modelling various phenomena [8,15,27,33]. Here we consider the scalar FDE C t 0 D β u(t) = g (t, u(t)) , t 0 t T, u(t 0 ) = u 0 , (1.1) where 0 < β < 1, g : [t 0 , T ]× → and C t 0 D β u(t) is the fractional derivative in the Caputo sense -cf.…”

Section: Introductionmentioning

confidence: 99%