# Computational Solutions of Distributed Order Reaction-Diffusion Systems Associated with Riemann-Liouville Derivatives

@article{Saxena2015ComputationalSO, title={Computational Solutions of Distributed Order Reaction-Diffusion Systems Associated with Riemann-Liouville Derivatives}, author={Ram K. Saxena and Arak M. Mathai and Hans J. Haubold}, journal={Axioms}, year={2015}, volume={4}, pages={120-133} }

This article is in continuation of the authors research attempts to derive computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative as space derivative. This article presents computational solutions of distributed order fractional reaction-diffusion equations associated with Riemann-Liouville derivatives of fractional orders as the time-derivatives and Riesz-Feller fractional…

## Topics from this paper

## 9 Citations

Computable Solutions of Fractional Reaction-Diffusion Equations Associated with Generalized Riemann-Liouville Fractional Derivatives of Fractional Orders

- Mathematics, Physics
- 2015

This paper is in continuation of the authors’ recently published paper (Journal of Mathematical Physics 55(2014)083519) in which computational solutions of an unified reactiondiffusion equation of…

Solution of fractional Distributed Order Reaction-Diffusion Systems with Sumudu Transform

- Materials Science, Mathematics
- 2017

Finding the solutions of some fractional differential equations, many of which used to be hard if not nearly untractable, is among the hottest quests in the fractional calculus field, nowadays. …

Analysis and numerics of traveling waves for asymmetric fractional reaction-diffusion equations

- Physics, Mathematics
- 2014

We consider a scalar reaction-diffusion equation in one spatial dimension with bistable nonlinearity and a nonlocal space-fractional diffusion operator of Riesz-Feller type. We present our analytical…

Approximate solution of space and time fractional higher order phase field equation

- Mathematics
- 2018

Abstract This paper is concerned with a class of space and time fractional partial differential equation (STFDE) with Riesz derivative in space and Caputo in time. The proposed STFDE is considered as…

Generalized Langevin Equation and the Prabhakar Derivative

- Mathematics
- 2017

We consider a generalized Langevin equation with regularized Prabhakar derivative operator. We analyze the mean square displacement, time-dependent diffusion coefficient and velocity autocorrelation…

Applications of Distributed-Order Fractional Operators: A Review

- Computer Science, MedicineEntropy
- 2021

This review article is intended to provide the reader a road map to understand the early development of DOFC and the progressive evolution and application to the modeling of complex real-world problems.

A new derivative with normal distribution kernel: Theory, methods and applications

- Mathematics
- 2017

New approach of fractional derivative with a new local kernel is suggested in this paper. The kernel introduced in this work is the well-known normal distribution that is a very common continuous…

Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws

- Mathematics
- 2017

Abstract The nature is very complex to model with mathematical equations. Some physical problems found in nature could follow the power law; other could follow the Mittag–Leffler law and other the…

Symmetric Fractional Diffusion and Entropy Production

- Mathematics, Computer ScienceEntropy
- 2016

This paper eliminates pseudo propagation by employing a similar evolution equation that imposes spatial unimodal symmetry on evolving PDFs and Contrary to initial expectations, familiar peculiarities emerge despite the imposed symmetry, but they have a distinct character.

## References

SHOWING 1-10 OF 75 REFERENCES

Distributed order reaction-diffusion systems associated with Caputo derivatives

- Physics, Mathematics
- 2014

This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and…

Further solutions of fractional reaction-diffusion equations in terms of the H-function

- Mathematics, Computer ScienceJ. Comput. Appl. Math.
- 2011

This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation associated with the Caputo derivative as the time-derivative and Riesz-Feller fractional…

The fundamental solution of the space-time fractional diffusion equation

- Mathematics, Physics
- 2007

We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from the standard diffusion equation by replacing the second-order space derivative with a…

Nonlinear oscillations and stability domains in fractional reaction-diffusion systems

- Mathematics
- 2007

We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the…

Mathematical modeling of pattern formation in sub- and supperdiffusive reaction-diffusion systems

- Physics, Mathematics
- 2006

This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example,…

Fractional Reaction-Diffusion Equations

- Physics, Mathematics
- 2006

In a series of papers, Saxena et al. (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of…

Exact solutions of triple-order time-fractional differential equations for anomalous relaxation and diffusion I: The accelerating case

- Mathematics
- 2011

In recent years the interest around the study of anomalous relaxation and diffusion processes is increased due to their importance in several natural phenomena. Moreover, a further generalization has…

DISTRIBUTED ORDER FRACTIONAL SUB-DIFFUSION

- Mathematics, Physics
- 2003

A distributed order fractional diffusion equation is considered. Distributed order derivatives are fractional derivatives that have been integrated over the order of the derivative within a given…

Solution of a modified fractional diffusion equation

- Mathematics
- 2006

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005)…

Reaction-Diffusion Systems and Nonlinear Waves

- Mathematics, Physics
- 2006

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne et al.…