Regularized fractional derivatives in Colombeau algebra
Authors
Abstract:
The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to a nonlinear heat equation illustrating the application of the theory.
similar resources
regularized fractional derivatives in colombeau algebra
the present study aims at indicating the existence and uniqueness result of system in extended colombeaualgebra. the caputo fractional derivative is used for solving the system of odes. in addition, rieszfractional derivative of colombeau generalized algebra is considered. the purpose of introducing rieszfractional derivative is regularizing it in colombeau sense. we also give a solution to a n...
full textSolving fractional evolution problem in Colombeau algebra by mean generalized fixed point
The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$ for the real $qin (0,1)$ with the initial value $u(0)=u_{0}intilde{R}$, where $tilde{R}$ is the set of all generalized real numbers and $A$ is an operator defined from $mathcal G$ into itself. Here the Caputo fractional derivative $D^{q}_c$ is used i...
full textThe Ultrarelativistic Reissner Nordstrøm Field in the Colombeau Algebra
The electromagnetic field of the ultrarelativistic Reissner Nordstrøm Solution shows the physically highly unsatisfactory property of a vanishing field tensor but a nonzero, i.e. δ-like, energy density. The aim of this work is to analyse this situation from a mathematical point of view, using the framework of Colombeau’s theory of nonlinear generalized functions. It is shown that the physically...
full textThe Ultrarelativistic Reissner Nordstrrm Field in the Colombeau Algebra
The electromagnetic eld of the ultrarelativistic Reissner Nordstrrm Solution shows the physically highly unsatisfactory property of a vanishing eld tensor but a nonzero, i.e.-like, energy density. The aim of this work is to analyse this situation from a mathematical point of view, using the framework of Colombeau's theory of nonlinear generalized functions. It is shown that the physically unsat...
full textOn Systems of Linear Algebraic Equations in the Colombeau Algebra
From the fact that the unique solution of a homogeneous linear algebraic system is the trivial one we can obtain the existence of a solution of the nonhomogeneous system. Coefficients of the systems considered are elements of the Colombeau algebra of generalized real numbers. It is worth mentioning that the algebra is not a field.
full textExistence/uniqueness of solutions to Heat equation in extended Colombeau algebra
This work concerns the study of existence and uniqueness to heat equation with fractional Laplacian dierentiation in extended Colombeau algebra.
full textMy Resources
Journal title
volume 7 issue 1
pages 279- 287
publication date 2016-02-18
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023