Domain coarsening in a subdiffusive Allen–Cahn equation

On generalized boundary value problems for a class of fractional differential inclusions

“…These kind of problems, coming from applied sciences, describe anomalous diffusion in disordered materials or with memory effects. For instance, the first equation is a perturbation by means of a nonlocal forcing term of the diffusion of particles verifying a generalized Fick's second law, for other kind of perturbation we refer to [1] and [32]. Important applications include viscoelasticity and seismic-wave theory, diffusion in turbulent plasma, fractal media and porous media (see, e.g., [19] and the references therein).…”

“…Important applications include viscoelasticity and seismic-wave theory, diffusion in turbulent plasma, fractal media and A u t h o r ' s C o p y porous media (see, e.g., [19] and the references therein). We consider a perturbed equation in the multidimensional case, like in [1] and [32], but in our case the forcing term is nonlocal. A periodic condition is associated to the system.…”

Extension of Cubic B-Spline for Solving the Time-Fractional Allen–Cahn Equation in the Context of Mathematical Physics

“…Ψ and φ are smooth and continuous functions with first order derivatives. Domain coarsening in a sub-diffusive ACE in terms of the Seki-Lindenberg sub diffusion reaction model was studied by Hamed and Nepomnyashchy [25]. Different types of specific solutions from first integral, (G ′ /G) expansion and the exp-function methods were explored by Güner et al [26].…”

A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic B-spline functions

“…The exact solution of space-time fractional ACE was discussed in [22] by means of a fractional subdiffusion method. The authors in [23] studied the coarsening of domains in a subdiffusive ACE in the context of the Seki-Lindenberg subdiffusion-reaction model. Yasar and Giresunlu [24] examined the exact solution of nonlinear space-time fractional ACE using (Ǵ G .…”