相关论文: The fractional d'Alembert's formulas

The goal of this communication is to propose a generalized notion of the "traditional derivative". This generalization includes the fractional derivatives such as the Riemann-Liouville, Gruenwald-Letnikov, Weyl, Riesz, Caputo, Marchaud…

We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce…

In this paper, through the introduction of partial multiple weights, we firstly study the related Rubio de Francia extrapolation theorem within the framework of partial Muckenhoupt classes and further obtain the corresponding extrapolation…

We introduce a more general discrete fractional operator, given by convex linear combination of the delta and nabla fractional sums. Fundamental properties of the new fractional operator are proved. As particular cases, results on delta and…

In this article we would like to consider some approaches to non-integer integro-differentiations and its implementation in computer algebra system Wolfram Mathematics.

We analyze solvability of a special form of distributed order fractional differential equations within the space of tempered distributions supported by the positive half-line.

We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the…

In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results.…

We give a proper fractional extension of the classical calculus of variations by considering variational functionals with a Lagrangian depending on a combined Caputo fractional derivative and the classical derivative. Euler-Lagrange…

A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.

We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet boundary conditions. We prove the uniform convergence of the…

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…

We review the language of differential forms and their applications to Riemannian Geometry with an orientation to General Relativity. Working with the principal algebraic and differential operations on forms, we obtain the structure…

In this paper we investigate fractional differential equations with Hilfer fractional derivative of order $1<\gamma<2$ and type $\delta \in [0,1]$ in a Banach space. We introduce a family of general fractional cosine operator functions of…

We consider the integral and derivative operators of tempered fractional calculus, and examine their analytic properties. We discover connections with the classical Riemann-Liouville fractional calculus and demonstrate how the operators may…

We present a systematic method to derive an ordinary differential equation for any Feynman integral, where the differentiation is with respect to an external variable. The resulting differential equation is of Fuchsian type. The method can…

We present a fractional superspace formulation of the centerless parasuper-Viraso-ro and fractional super-Virasoro algebras. These are two different generalizations of the ordinary super-Virasoro algebra generated by the infinitesimal…

We briefly review our recent results on the geometry of nonholonomic manifolds and Lagrange--Finsler spaces and fractional calculus with Caputo derivatives. Such constructions are used for elaborating analogous models of fractional gravity…

Fractional derivatives are generalization to classical integer-order derivatives. The rules which are true for classical derivative need not hold for the fractional derivatives, for example, we cannot simply add the fractional orders…

In this study , we display a generalization of Darbos fixed point theorem , by using the use of a freshly made contraction operator and that we use to study the solvability of an integral equation involving the weighted fractional integral…