Related papers: On the material time derivative of volume, surface…

"Acoustic spacetimes", in which techniques of differential geometry are used to investigate sound propagation in moving fluids, have attracted considerable attention over the last few decades. Most of the models currently considered in the…

In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…

Many technological processes include preparing some special materials adhering to a product surface. For example, this problem is important for the magnetic tape producing, wire adhering, etc. For a surface withdrawn from the molten metal…

Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…

A possibility to represent the standard model of fundamental particles covariant derivatives by means of approximate generalized fractional Riemann-Liouville derivatives of multifractal time and space model is shown.

In this paper, we use the fractional calculus to discuss the fractional mechanics, where the time derivative is replaced with the fractional derivative of order $\nu$. We deal with the motion of a body in a resisting medium where the…

We investigate the behavior of the time derivatives of the solution to a linear time-fractional, advection-diffusion-reaction equation, allowing space- and time-dependent coefficients as well as initial data that may have low regularity.…

Based on the idea of emergent spacetime, we consider the possibility that the material underlying our spacetime is modelled by a fluid. We are particularly interested in possible connections between the geometrical properties of the…

I propose that Physics should be formulated using minimal mathematical structure, beginning with its foundational arena: spacetime. This paper opens with a concise overview of several research directions explored in previous work. Among…

We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are proved. Linear conformable differential equations with…

The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…

This paper continues the author's previous work on a limit-free algebraic-geometric construction of the derivative in the class of polynomial functions and extends the proposed framework to elementary functions. Derivatives of rational…

In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…

A particular science is not only defined by its object of study, but also by the point of view and method under which it considers that same object. Taking space and time as an illustrative example, our main aim here is to bring out an…

Advective transport of scalar quantities through surfaces is of fundamental importance in many scientific applications. From the Eulerian perspective of the surface it can be quantified by the well-known integral of the flux density. The…

We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Kr\"uhner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily…

In this article we review existing literature on dynamic copulas and then propose an n-copula which varies in time and space. Our approach makes use of stochastic differential equations, and gives rise to a dynamic copula which is able to…

We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional differentiation and fractional integration) are then…

In this paper we propose a space-time framework for the computation of periodic flows. We employ the isogeometric analysis framework to achieve higher-order smoothness in both space and time. The discretization is performed using…

We study a system of partial differential equations with integer and fractional derivatives arising in the study of forced oscillatory motion of a viscoelastic rod. We propose a new approach considering a quotient of relations appearing in…