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Fractional Reaction-Diffusion Equation [PDF]

The Journal of Chemical Physics, 2003
A fractional reaction-diffusion equation is derived from a continuous time random walk model when the transport is dispersive. The exit from the encounter distance, which is described by the algebraic waiting time distribution of jump motion, interferes ...
Seki, Kazuhiko, Tachiya, M., Wojcik, Mariusz   +2 more
core   +3 more sources

Fractional reaction-diffusion equations [PDF]

Astrophysics and Space Science, 2007
In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995 ...
A. Compte, A. Erdélyi, A. Erdélyi, A. Erdélyi, A. Erdélyi, A. Erdélyi, A. M. Mathai, A. Wiman, A.A. Kilbas, A.M. Mathai, A.M. Mathai, A.P. Prudnikov, B.I. Henry, B.I. Henry, B.I. Henry, C. Tsallis, C. Tsallis, D. Del-Castillo-Negrete, D. Del-Castillo-Negrete, E.M. Wright, E.M. Wright, E.M. Wright, G. Nicolis, H. Haken, H. J. Haubold, H. Wilhelmsson, H.J. Haubold, H.J. Haubold, J.D. Murray, K.B. Oldham, K.S. Miller, L. Debnath, M. Caputo, M.G. Mittag-Leffler, M.G. Mittag-Leffler, M.M. Dzherbashyan, M.M. Dzherbashyan, R. K. Saxena, R. Metzler, R. Metzler, R.K. Saxena, R.K. Saxena, R.K. Saxena, R.M. Kulsrud, S. Jespersen, S.G. Samko, W. Hundsdorfer, Y. Kuramoto   +47 more
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A Domain Decomposition Method for Time Fractional Reaction-Diffusion Equation [PDF]

The Scientific World Journal, 2014
The computational complexity of one-dimensional time fractional reaction-diffusion equation is O(N2M) compared with O(NM) for classical integer reaction-diffusion equation. Parallel computing is used to overcome this challenge.
Chunye Gong, Weimin Bao, Guojian Tang, Yuewen Jiang, Jie Liu   +4 more
doaj   +2 more sources

Analytical solutions and dynamic behavior of conformable fractional reaction-diffusion systems [PDF]

Scientific Reports
This study presents an analytical investigation of fractional reaction-diffusion systems within the framework of the conformable fractional operator. The conformable operator provides a simplified yet powerful mathematical tool for modeling fractional ...
Azzh Saad Alshehry, Rasool Shah, Aisha M. Alqahtani   +2 more
doaj   +2 more sources

Dynamics of Fractional Delayed Reaction-Diffusion Equations

Entropy, 2023
The long-term behavior of the weak solution of a fractional delayed reaction–diffusion equation with a generalized Caputo derivative is investigated.
Linfang Liu, Juan J. Nieto
doaj   +3 more sources

Solution of generalized fractional reaction-diffusion equations [PDF]

Astrophysics and Space Science, 2007
This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and ...
A. Compte, A. Erdélyi, A. Erdélyi, A. Erdélyi, A. Erdélyi, A. M. Mathai, A. Wiman, A.A. Kilbas, A.M. Mathai, A.P. Prudnikov, B.I. Henry, B.I. Henry, B.I. Henry, D. Del-Castillo-Negrete, E.M. Wright, E.M. Wright, E.M. Wright, G. Nicolis, H. Haken, H. J. Haubold, H. Wilhelmsson, H.J. Haubold, H.J. Haubold, I. Podlubny, I.M. Gelfand, K.B. Oldham, K.S. Miller, M. Caputo, M.G. Mittag-Leffler, M.G. Mittag-Leffler, M.M. Dzherbashyan, M.M. Dzherbashyan, R. K. Saxena, R. Metzler, R. Metzler, R.K. Saxena, R.K. Saxena, R.K. Saxena, R.K. Saxena, S. Jespersen, S.G. Samko, T.D. Frank, Yu.A. Brychkov   +42 more
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Front propagation in hyperbolic fractional reaction-diffusion equations [PDF]

Physical Review E, 2005
From the continuous-time random walk scheme and assuming a Lévy waiting time distribution typical of subdiffusive transport processes, we study a hyperbolic reaction-diffusion equation involving time fractional derivatives.
Méndez López, Vicenç, Ortega Cejas, Vicente   +1 more
core   +8 more sources

Well-posedness of time-fractional, advection-diffusion-reaction equations [PDF]

Fractional Calculus and Applied Analysis, 2019
We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our
Ali, Raed, Knio, Omar, McLean, William, Mustapha, Kassem   +3 more
core   +4 more sources

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

Axioms, 2014
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 ...
Ram K. Saxena, Arak M. Mathai, Hans J. Haubold   +2 more
doaj   +5 more sources

On the Speed of Spread for Fractional Reaction-Diffusion Equations [PDF]

International Journal of Differential Equations, 2009
The fractional reaction diffusion equation u_t + Au = g(u) is discussed, where A is a fractional differential operator on the real line with order \alpha between 0 and 2, the C^1 function g vanishes at 0 and 1, and either g is non-negative on (0,1) or g <
Engler, Hans
core   +7 more sources