Related papers: Revisiting Fractional Cosmology
This paper continues the development of a discrete space-time concept that is recently used in the explanation of the cosmological constant. Instead of order estimation, a more theoretical treatment of the theory is introduced. Based on the…
We study the possibility to obtain cosmological late-time acceleration from a geometry changing with the scale, in particular, in the so-called multifractional theories with $q$-derivatives and with weighted derivatives. In the theory with…
In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
Higher derivative scalar field theories have received considerable attention for the potentially explanations of the initial state of the universe or the current cosmic acceleration which they might offer. They have also attracted many…
We study the introduction of holonomy corrections in $f(R)$ gravity. We will show that there are infinitely many ways, as many as canonical transformations, to introduce this kind of corrections, depending on the canonical variables (two…
The dynamics of a universe with an anti-gravitating contribution to the matter content is examined. The modified Friedmann equations are derived, and it is shown that anti-gravitating radiation is the slowest component to dilute when the…
The Hamiltonian approach to General Relativity is developed similarly to the Wheeler-DeWitt Hamiltonian cosmology, where the cosmological scale factor is treated as a time-like dynamic variable and its canonical momentum is considered as an…
In this work, we study cosmological and astrophysical applications of the recently proposed generalized hybrid metric-Palatini gravity theory, which combines features of both the metric and the Palatini approaches to the variational method…
This letter extends previous findings on the modified Schr\"odinger evolution inspired by quantum gravity phenomenology. By establishing a connection between this approach and fractional quantum mechanics, we provide insights into a…
By fractional relativity we mean a theoretical framework to study physics with the dispersion relation $E^{\alpha}=m^{\alpha}c^{2\alpha}+p^{\alpha}c^{\alpha}$, which recovers special relativity at $\alpha=2$. One such framework is…
In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional…
In this article we present the cosmological equivalence between the relativistic Finsler-Randers cosmology, with dark energy and modified gravity constructions, at the background level. Starting from a small deviation from the quadraticity…
It has been shown that at the semi-classical order, gravitational theories with quantum fluctuations can be effectively recast as modified theories of gravity with non-minimal gravity-matter couplings. We proceed from an observational…
We analyze the quantum dynamics of the fractional-time Jaynes-Cummings model using a recent unitary framework for the fractional-time Schr\"odinger equation. We examine how the fractional derivative order $\alpha$ influences non-classical…
Using a dynamical system approach we study the cosmological phase space of the generalized hybrid metric-Palatini gravity theory, characterized by the function $f\left(R,\mathcal R\right)$, where $R$ is the metric scalar curvature and…
In a series of recent papers we put forward a ``fractional gravity'' framework striking an intermediate course between a modified gravity theory and an exotic dark matter (DM) scenario, which envisages the DM component in virialized halos…
We reconcile seemingly conflicting statements in the literature about the behavior of cosmological solutions in modified theories of gravity where the Einstein-Hilbert Lagrangian for gravity is modified by the addition of a function of the…
A two dimensional matter coupled model of quantum gravity is studied in the Dirac approach to constrained dynamics in the presence of a cosmological constant. It is shown that after partial fixing to the conformal gauge the requirement of a…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…