Related papers: Joining Spacetimes on Fractal Hypersurfaces
We investigate the expanding and collapsing regions by taking two well-known spherically symmetric spacetimes. For this purpose, the general formalism is developed by using Israel junction conditions for arbitrary spacetimes. This has been…
We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows…
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…
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…
Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
Fractional calculus is a couple of centuries old, but its development has been less embraced and it was only within the last century that a program of applications for physics started. Regarding quantum physics, it has been only in the…
Applying the distributional formalism to study the dynamics of thin shells in general relativity, we regain the junction equations for matching of two spherically symmetric spacetimes separated by a singular hypersurface. In particular, we…
We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display…
In this paper, we discuss gravitational collapse of spherically symmetric spacetimes. We derive a general formalism by taking two arbitrary spherically symmetric spacetimes with $g_{00}=1$. Israel's junction conditions are used to develop…
I present the junction conditions for F(R) theories of gravity and their implications: the generalized Israel conditions and equations. These junction conditions are necessary to construct global models of stars, galaxies, etc., where a…
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…
We present the GRjunction package which allows boundary surfaces and thin-shells in general relativity to be studied with a computer algebra system. Implementing the Darmois-Israel thin shell formalism requires a careful selection of…
Fractional calculus represents a natural tool for describing relativistic phenomena in pseudo-Euclidean space-time. In this study, Fractional modified special relativity is presented. We obtain fractional generalized relation for the time…
We investigate some basic applications of Fractional Calculus (FC) to Newtonian mechanics. After a brief review of FC, we consider a possible generalization of Newton's second law of motion and apply it to the case of a body subject to a…
Taking advantage of the conformal equivalence of f(R) theories of gravity with General Relativity coupled to a scalar field we generalize the Israel junction conditions for this class of theories by direct integration of the field…
We present a general method to derive the appropriate Darmois-Israel junction conditions for gravitational theories with higher-order derivative terms by integrating the bulk equations of motion across the singular hypersurface. In higher…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old…
Supersymmetric (pseudo-classical) mechanics has recently been generalized to {\it fractional}\/ supersymmetric mechanics. In such a construction, the action is invariant under fractional supersymmetry transformations, which are the…