Related papers: Fractal Sumudu Transform and Economic Models

A way to add an extra dimension is briefly discussed.

Dynamical systems involving non-local derivative operators are of great importance in Mathematical analysis and applications. This article deals with the dynamics of fractional order systems involving Caputo derivatives. We take a review of…

The paper is devoted to the development of control procedures with a guide for conflict-controlled dynamical systems described by ordinary fractional differential equations with the Caputo derivative of an order $\alpha \in (0, 1).$ For the…

In this article, the existence and uniqueness about the solution for a class of stochastic fractional-order differential equation systems are investigated, where the fractional derivative is described in Caputo sense. The fractional…

In this paper, we propose a fractional time extension of the Quan tum Master Equation. We introduce a Caputo-type fractional derivative in time as an extension of the exponential decay of the Lindblad framework through the incorporation of…

We use the fractional integrals to describe fractal media. We consider the fractal media as special ("fractional") continuous media. We discuss the possible experimental testing of the continuous medium model for fractal media that is…

Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition…

We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one of them an approximation formula is…

The question of a possible excitation and emergence of fractional type dynamics, as a more realistic framework for understanding emergence of complex systems, directly from a conventional integral order dynamics, in the form a continuous…

We develop a theory of separable ring extensions and separable functors for nonunital rings in the setting of firm modules. We prove nonunital analogues of classical results on functorial separability and semisimplicity, and apply these…

In the present paper, we discuss solvability questions of a non-local problem with integral form transmitting conditions for diffusion-wave equation with the Caputo fractional derivative in a domain bounded by smooth curves. The uniqueness…

Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the…

It is an established fact that a finite difference operator approximates a derivative with a fixed algebraic rate of convergence. Nevertheless, we exhibit a new finite difference operator and prove it has spectral accuracy. Its rate of…

For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of the operator theory in fractional Sobolev spaces. Our framework provides a feasible extension of the classical Caputo and the…

In this paper we introduce a two-parameter family of Mehler kernels and connect them to a class of Baouendi-Grushin flows in fractal dimension. We also highlight a link with a geometric fully nonlinear equation and formulate two questions.

Many different types of fractional calculus have been proposed, which can be organised into some general classes of operators. For a unified mathematical theory, results should be proved in the most general possible setting. Two important…

There are many functions which are continuous everywhere but not differentiable at some points, like in physical systems of ECG, EEG plots, and cracks pattern and for several other phenomena. Using classical calculus those functions cannot…

In this document, we describe the fractal structure of the Netsukuku topology. Moreover, we show how it is possible to use the QSPN v2 on the high levels of the fractal.

The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct Fredholm modules on post critically finite fractals by regular harmonic structures. The modules are…

Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We…