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, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation...

In the present paper, we study Cauchy-Dirichlet problem to a nonlocal nonlinear diffusion equation with polynomial nonlinearities $$\mathcal {D}_{0|t}^{\alpha }u+(-\varDelta )^s_pu=\gamma |u|^{m-1}u+\mu |u|^{q-2}u,\,\gamma ,\mu \in \mathbb {R},\,m>0,q>1,$$ involving time-fractional Caputo derivative }$$ and space-fractional p-Laplacian operator $$(-\varDelta )^s_p$$ . We give simple proof of co...

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, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation...

This note presents a Laplace transform approach in the determination of the Lagrange multiplier when the variational iteration method is applied to time fractional heat diffusion equation. The presented approach is more straightforward and allows some simplification in application of the variational iteration method to fractional differential equations, thus improving the convergence of the suc...

Abst ract The Ehrenfest model is considered as a good example of a Markov chain. I prove in this paper that the time-fractional diffusion process with drift towards the origin, is a natural generalization of the modified Ehrenfest model. The corresponding equation of evolution is a linear partial pseudo-differential equation with fractional derivatives in time, the orders lying between 0 and 1....

This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables and eigenfunction expansions in time and space are used to write strong solutions. Finally, stochastic solutions are written in terms of an inverse subordinator.