The cauchy problem for the multi-time ractional diffusion equation

In this work, we study the following problem: find a regular solution и = u(x, y

A Priori Estimates for Solutions of Boundary Value Problems for Fractional-Order Equations

We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.Comment: 10 pages, no figur

Boundary value problems for the diffusion equation of the variable order in differential and difference settings

Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori estimates for these problems exactly as in the classical case. The credibility of the obtained results is verified by performing numerical calculations for a test problem.Comment: 19 pages. Presented at the 4-th IFAC Workshop on Fractional Differentiation and Its Applications, Badajoz, Spain, October 18-20, 201

Approximate Solutions to Fractional Subdiffusion Equations: The heat-balance integral method

The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile with unknown coefficients and the concept of penetration (boundary layer). The prescribed profile satisfies the boundary conditions imposed by the boundary layer that allows its coefficients to be expressed through its depth as unique parameter. The integral approach to the fractional subdiffusion equation suggests a replacement of the real distribution function by the approximate profile. The solution was performed with Riemann -Liouville time-fractional derivative since the integral approach avoids the definition of the initial value of the time-derivative required by the Laplace transformed equations and leading to a transition to Caputo derivatives. The method is demonstrated by solutions to two simple fractional subdiffusion equations (Dirichlet problems): 1) Time-Fractional Diffusion Equation, and 2) Time-Fractional Drift Equation, both of them having fundamental solutions expressed through the M-Write function. The solutions demonstrate some basic issues of the suggested integral approach, among them: a) Choice of the profile, b) Integration problem emerging when the distribution (profile) is replaced by a prescribed one with unknown coefficients; c) Optimization of the profile in view to minimize the average error of approximations; d) Numerical results allowing comparisons to the known solutions expressed to the M-Write function and error estimations.Comment: 15 pages, 7 figures, 3 table

The cauchy problem for the multi-time ractional diffusion equation

In this work, we study the following problem: find a regular solution и = u(x, y

The Spiritual and Moral Dimension of Modern Theatre The Philosophical and Linguistic Analysis of Rhapsody for the Theatre by A. Badiou

The paper investigates the problems of interconnection between performing arts, politics and the machinery of state, based on works of the famous French philosopher-post-modernist A. Badiou. The analogy between theatre and politics, proposed by him, analyzed when applied to Russian culture and interaction with political realia of past and present. An attempt is made to compare politics and theatre as phenomena that have much in common from the conceptual, structural and functional points of view. The paper also brings up the problem of the status and the role of a person and a society at large as components of creative process, some aspects concerning the extent of influence that theatre makes on both individual consciousness and collective thinking and their view of the world

Multi-time fractional diffusion equation

We construct a fundamental solution of a multi-time diffusion equation with the Dzhrbashyan-Nersesyan fractional differentiation operator with respect to the time variables. We give a representation for a solution of the Cauchy problem and prove the uniqueness theorem in the class of functions of fast growth. The corresponding results for equations with Riemann-Liouville and Caputo derivatives are obtained as particular cases of the proved assertions

Perfomance in Philosophy: One Man Play or a Living Personified Thought

The paper investigates the problems of convergence of philosophy and theatre, the amount of actors' contribution to creating or performing oral philosophical text, to analyze the professional philosopher's (or a teacher of philosophy) methods that are used to "vividly reproduce" the philosophical views in the minds of the listening audience, which brings together the art of philosopher's speech and performing arts. The analysis of K. Stanislayski, M. Chekhov, Jerzy Grotowski's works on the art of acting, along with the works on the phenomenon of theatre (namely, of A. Badiou), and a range of classical philosophical works, that are analyzed in terms of their performing potential, could contribute to highlighting the central issue: what really makes oral philosophical text expressive. A possible answer is the image of the thought that has its specific space or stage for performance, set by philosopher himself by "drama" means. The unity of philosophy and theatre has a bright future ahead. It is already obvious that the process of thinking alongside acting and happening will become a central point of a public thinker's activity