Related papers: Joining Spacetimes on Fractal Hypersurfaces
In this study, we explore the field of physics through the lens of fractional dimensionality. We propose that space is not confined to integer dimensions alone, but can also be understood as a superposition of spaces that exist between…
In this manuscript, we generalize F-calculus to apply it on fractal Tartan spaces. The generalized standard F-calculus is used to obtain the integral and derivative of the functions on the fractal Tartan with different dimensions. The…
The formulation of gravity theory is considered where space-time is a 4-dimensional surface in flat ten-dimensional space. The possibility of using the "external" time (the time of ambient space) in this approach is investigated. The…
Breast cancer exhibits intricate morphological and dynamical heterogeneity across cellular, tissue, and tumor scales, posing challenges to conventional modeling approaches that fail to capture its nonlinear, self-similar, or self-affine,…
Generalized Feller theory provides an important analog to Feller theory beyond locally compact state spaces. This is very useful for solutions of certain stochastic partial differential equations, Markovian lifts of fractional processes, or…
Fractional supersymmetry denotes a generalisation of supersymmetry which may be constructed using a single real generalised Grassmann variable, $\theta = \bar{\theta}, \, \theta^n = 0$, for arbitrary integer $n = 2, 3, ...$. An explicit…
We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…
This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing equations with local fractional derivative.
Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integro-differentiation. The…
Hypersurfaces of arbitrary causal character embedded in a spacetime are studied with the aim of extracting necessary and sufficient free data on the submanifold suitable for reconstructing the spacetime metric and its first derivative along…
In this paper we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We…
Methods from the geometry of nonholonomic manifolds and Lagrange-Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and fractional Lagrange mechanics. The geometric…
Non-Newtonian calculus naturally unifies various ideas that have occurred over the years in the field of generalized thermostatistics, or in the borderland between classical and quantum information theory. The formalism, being very general,…
Viscoelasticity and related phenomena are of great importance in the study of mechanical properties of material especially, biological materials. Certain materials show some complex effects in mechanical tests, which cannot be described by…
The optical model is a fundamental tool to describe scattering processes in nuclear physics. The basic input is an optical model potential, which describes the refraction and absorption processes more or less schematically. Of special…
We prove that any given function can be smoothly approximated by functions lying in the kernel of a linear operator involving at least one fractional component. The setting in which we work is very general, since it takes into account…
General fractional calculus offers an elegant and self-consistent path toward the generalization of fractional calculus to an enhanced class of kernels. Prabhakar's theory can be thought of, to some extent, as an explicit realization of…
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…
The aim of this work is to introduce the main concepts of Fractional Calculus, followed by one of its application to classical electrodynamics, illustrating how non-locality can be interpreted naturally in a fractional scenario. In…
There are many resources useful for processing images, most of them freely available and quite friendly to use. In spite of this abundance of tools, a study of the processing methods is still worthy of efforts. Here, we want to discuss the…