Related papers: Revisiting Fractional Cosmology
Topological defects in the framework of effective quantum gravity model are investigated, based on the hypothesis of an effective fractal dimension of the universe. This is done by using Caputo fractional derivatives to determine the…
Building on earlier work, we discuss a general framework for exploring the cosmological dynamics of Higher Order Theories of Gravity. We show that once the theory of gravity has been specified, the cosmological equations can be written as a…
The purpose of this paper is to investigate the oscillatory behavior of the universe through a Schr\"odinger-like Friedmann equation and a modified gravitational background described by the theory of f (R) gravity. The motivation for this…
The current cosmic time evolution of the Universe is described by the General Relativity theory when a cosmological principle is considered under a flat space time landscape. The set of known as Friedmann equations, contain the principles…
In the Newtonian limit of general relativity force acting on a test mass in a central gravitational field is conventionally defined by the attractive Newtonian gravity (inverse square) term plus a small repulsive cosmological force, which…
The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future…
Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher dimensional approaches and…
Modified gravity theories can be used for the description of homogeneous and isotropic cosmological models through the corresponding field equations. These can be cast into systems of autonomous differential equations because of their sole…
The theory of fractional calculus is attracting a lot of attention from mathematicians as well as physicists. The fractional generalisation of the well-known ordinary calculus is being used extensively in many fields, particularly in…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
In this paper, we investigate and analyze the cosmological dynamics of the universe, with an effect of modified $f(R)$ gravity emerging at cosmological scale. We choose the Einstein frame as a physical frame. We consider phase portraits of…
We propose an analytic procedure that allows to determine quantitatively the deviation in the behavior of cosmological perturbations between a given f(R) modified gravity model and a LCDM reference model. Our method allows to study…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
In this paper, the dynamical system analysis has been performed to analyze the dynamical behavior of the Universe in $f(R,L_m,T)$ gravity with a scalar field. A well motivated potential function and the linear form of the functional…
We examine the dynamical behavior of matter coupled to gravity in the context of a linear Klein-Gordon equation coupled to a Friedman-Robertson-Walker metric. The resulting ordinary differential equations can be decoupled, the effect of…
Using dynamical system analysis, we explore the cosmology of theories of order up to eight order of the form $f(R, \Box R)$. The phase space of these cosmology reveals that higher-order terms can have a dramatic influence on the evolution…
Within the framework of fractional calculus with variable order the evolution of space in the adiabatic limit is investigated. Based on the Caputo definition of a fractional derivative using the fractional quantum harmonic oscillator a…
For the fourth-order teleparallel $f\left(T,B\right) $ theory of gravity, we investigate the cosmological evolution for the universe in the case of a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker background space. We focus on…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
This is a first study of the cosmology of classical fractional gravity, a nonlocal proposal endowed with self-adjoint fractional d'Alembertian operators which serves as the basis for an ultraviolet-complete theory of quantum gravity. We…