Next Article in Journal
The Gromov–Wasserstein Distance: A Brief Overview
Previous Article in Journal
Matching the LBO Eigenspace of Non-Rigid Shapes via High Order Statistics
Article Menu

Export Article

Open AccessArticle
Axioms 2014, 3(3), 320-334; doi:10.3390/axioms3030320

Space-Time Fractional Reaction-Diffusion Equations Associated with a Generalized Riemann–Liouville Fractional Derivative

1
Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur 342005, India
2
Centre for Mathematical and Statistical Sciences, Peechi Campus, KFRI, Peechi 680653, Kerala, India
3
Department of Mathematics and Statistics, McGill University, Montreal H3A 2K6, Canada
4
Office for Outer Space Affairs, United Nations, P.O. Box 500, Vienna International Centre, Vienna 1400, Austria
*
Author to whom correspondence should be addressed.
Received: 24 March 2014 / Revised: 8 July 2014 / Accepted: 22 July 2014 / Published: 4 August 2014
View Full-Text   |   Download PDF [249 KB, uploaded 4 August 2014]

Abstract

This paper deals with the investigation of the computational solutions of a unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann–Liouville fractional derivative defined by others and the space derivative of second order by the Riesz–Feller fractional derivative and adding a function ɸ(x, t). The solution is derived by the application of the Laplace and Fourier transforms in a compact and closed form in terms of Mittag–Leffler functions. The main result obtained in this paper provides an elegant extension of the fundamental solution for the space-time fractional diffusion equation obtained by others and the result very recently given by others. At the end, extensions of the derived results, associated with a finite number of Riesz–Feller space fractional derivatives, are also investigated. View Full-Text
Keywords: fractional operators; fractional reaction-diffusion; Riemann-Liouville fractional derivative; Riesz-Feller fractional derivative; Mittag-Leffler function fractional operators; fractional reaction-diffusion; Riemann-Liouville fractional derivative; Riesz-Feller fractional derivative; Mittag-Leffler function
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Saxena, R.K.; Mathai, A.M.; Haubold, H.J. Space-Time Fractional Reaction-Diffusion Equations Associated with a Generalized Riemann–Liouville Fractional Derivative. Axioms 2014, 3, 320-334.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top