Related papers: A short introduction to local fractional complex a…
Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric…
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
We use generalized Taylor formulae in order to give some simple constructions in the real closure of an \ovfz. We deduce a new, simple quantifier elimination algorithm for \rcvfs and some theorems about constructible subsets of real…
The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this note, I discuss some aspects of this more general Fourier…
The paper describes different approaches to generalize the trapezoidal method to fractional differential equations. We analyze the main theoretical properties and we discuss computational aspects to implement efficient algorithms. Numerical…
We study generalized fractional $p$-Laplacian equations to prove local boundedness and H\"older continuity of weak solutions to such nonlocal problems by finding a suitable fractional Sobolev-Poincar\'e inquality.
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…
This article is part introduction and part survey to the mathematical area centered around local cohomology.
The aim of the present paper is to make some notes to the newly introduced conformable derivative as a type local fractional derivative and to present a surprising result about the relation between the conformable derivatives and the usual…
We introduce a general context involving a presheaf A and a subpresheaf B of A. We show that all previously considered cases of local analysis of generalized functions (defined from duality or algebraic techniques) can be interpretated as…
It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we…
In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced…
The subject of fractional calculus has witnessed rapid development over past few decades. In particular the area of fractional differential equations has received considerable attention. Several theoretical results have been obtained and…
The generalization of the the Yang-Baxter relation is proposed. In this generalization the spectral parameters of the particles change after the scattering. The corresponding algebraic structures are discussed. The corresponding action of…
In this paper, we study local systems of locally finite associative algebras over fields of characteristic p\ge0. We describe the perfect local systems and study the relation between them and their corresponding locally finite associative…
The Mittag-Leffler type functions arise naturally in the solution of fractional order integral and differential equations, especially in the investigations of the fractional generalization of the kinetic equation. This article introduces a…
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…
This is an exposition of some basic ideas in the realm of Global Inverse Function theorems. We address ourselves mainly to readers who are interested in the applications to Differential Equations. But we do not deal with those applications…
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…
We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of…