The paradigm of quantum cosmology through Dunkl fractional Laplacian operators and fractal dimensions

El-Nabulsi, Rami Ahmad; Anukool, Waranont

doi:10.1016/j.chaos.2022.113097

Cited by 13 publications

(2 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Once again, we look at specific cases as we analyze the fractional WDW equation and show how the results of this fractional model can help us understand the fascinating concepts of non-locality and memory property. In addition to our models herein, the reader may, however, consider other intriguing models like [58,[77][78][79][80] as well as [80][81][82][83][84].…”

Section: Introductionmentioning

confidence: 99%

Fractional Scalar Field Cosmology

Rasouli,

Cheraghchi,

Moniz

2024

Fractal Fract

View full text Add to dashboard Cite

Considering the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and the Einstein scalar field system as an underlying gravitational model to construct fractional cosmological models has interesting implications in both classical and quantum regimes. Regarding the former, we just review the most fundamental approach to establishing an extended cosmological model. We demonstrate that employing new methodologies allows us to obtain exact solutions. Despite the corresponding standard models, we cannot use any arbitrary scalar potentials; instead, it is determined from solving three independent fractional field equations. This article concludes with an overview of a fractional quantum/semi-classical model that provides an inflationary scenario.

show abstract

Section: Introductionmentioning

confidence: 99%

Fractional Scalar Field Cosmology

Rasouli,

Cheraghchi,

Moniz

2024

Fractal Fract

View full text Add to dashboard Cite

show abstract

“…Zhang, Deng and Karniadakis [22] presented new computational methods for the tempered fractional Laplacian equation on the homogeneous and nonhomogeneous generalized Dirichlet type boundary conditions. Other new developments of the tempered fractional Laplace operator can be found in [23][24][25][26][27][28][29][30][31]. The conception and properties of fractional conformable Caputo and Riemann-Liouville derivatives were formulated by Jarad et al [32].…”

Section: Introductionmentioning

confidence: 99%

Maximum Principle for Variable-Order Fractional Conformable Differential Equation with a Generalized Tempered Fractional Laplace Operator

Guan,

Zhang

2023

Fractal Fract

View full text Add to dashboard Cite

In this paper, we investigate properties of solutions to a space-time fractional variable-order conformable nonlinear differential equation with a generalized tempered fractional Laplace operatorby using the maximum principle. We first establish some new important fractional various-order conformable inequalities. With these inequalities, we prove a new maximum principle with space-time fractional variable-order conformable derivatives and a generalized tempered fractional Laplace operator. Moreover, we discuss some results about comparison principles and properties of solutions for a family of space-time fractional variable-order conformable nonlinear differential equations with a generalized tempered fractional Laplace operator by maximum principle.

show abstract

Fractional Elliptic Operators with Multiple Poles on Riemannian Manifold with Clifford Bundle

El-Nabulsi,

Anukool

2024

Adv. Appl. Clifford Algebras

View full text Add to dashboard Cite

The paradigm of quantum cosmology through Dunkl fractional Laplacian operators and fractal dimensions

Cited by 13 publications

References 43 publications

Fractional Scalar Field Cosmology

Fractional Scalar Field Cosmology

Maximum Principle for Variable-Order Fractional Conformable Differential Equation with a Generalized Tempered Fractional Laplace Operator

Fractional Elliptic Operators with Multiple Poles on Riemannian Manifold with Clifford Bundle

Contact Info

Product

Resources

About