Fractional Action Cosmology with Variable Order Parameter

El-Nabulsi, Rami Ahmad

doi:10.1007/s10773-016-3260-z

Cited by 45 publications

(49 citation statements)

References 94 publications

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“…Fractional action cosmology with variable order parameter was constructed in Ref. [96], where a large number of cosmological equations are obtained depending on the mathematical type of the fractional order parameter. This idea results on a number of cosmological scenarios and their dynamical consequences.…”

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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“…The role of standard Lagrangians, whose the kinetic and potential energy-like terms can easily be identified, has been well established in Classical Mechanics (CM) (e.g., [1][2][3][4][5]). On the other hand, the so-called non-standard Lagrangians, in which neither kinetic nor potential energy-like terms exist, have been introduced to CM in recent years (e.g., [6][7][8][9][10][11][12]). There are also null Lagrangians, whose two main characteristics are: (i) that they identically satisfy the Euler-Lagrange (E-L) equation, and (ii) that they can be expressed as the total derivative of any scalar function, called here a gauge function.…”

Section: Introductionmentioning

confidence: 99%

Non-standard Null Lagrangians and Forces in Classical Mechanics

Segovia¹,

Vestal²,

Musielak³

2022

Preprint

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Non-standard Lagrangians are a family of Lagrangians with terms that do not have clearly discernable energy-like forms. A special class among these Lagrangians are non-standard null Lagrangians and their gauge functions, which are used to introduce forces to the laws of dynamics. It is shown that the non-standard Lagrangian for the law of inertia is Galilean invariant but the forces resulting from the non-standard null Lagrangian are not Galilean invariant, except special only time-dependent forces.

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“…The procedure of finding these Lagrangians for given ODEs is called the inverse (or Helmholtz) problem of the calculus of variations [10,11]. There are different methods to find the standard [12][13][14][15][16] and nonstandard [15][16][17][18][19][20] Lagrangians. Generalized nonstandard Lagrangians can also be obtained [21] and applied to the ODEs, whose solutions are special functions of mathematical physics [22].…”

Section: Introductionmentioning

confidence: 99%