An operational matrix for solving time-fractional order Cahn-Hilliard equation

Extended Triangular Operational Matrix For Solving Fractional Population Growth Model

  In this paper, we apply the extended triangular operational matrices of fractional order to solve the fractional voltrra model for population growth of a species in a closed system. The fractional derivative is considered in the Caputo sense. This technique is based on generalized operational matrix of triangular functions. The introduced method reduces the proposed problem for solving a syst...

Sinc operational matrix method for solving the Bagley-Torvik equation

The aim of this paper is to present a new numerical method for solving the Bagley-Torvik equation. This equation has an important role in fractional calculus. The fractional derivatives are described based on the Caputo sense. Some properties of the sinc functions required for our subsequent development are given and are utilized to reduce the computation of solution of the Bagley-Torvik equati...

The Cahn-hilliard Equation

1. Steady states. There are many two component systems in which phase separation can be induced by rapidly cooling the system. Thus, if a two component system, which is spatially uniform at temperature T1, is rapidly cooled to a second sufficiently lower temperature T2, then the cooled system will separate into regions of higher and lower concentration. A phenomenological description of the beh...

The Cahn–Hilliard Equation

Analysis and Approximation of a Fractional Cahn-Hilliard Equation

We derive a Fractional Cahn-Hilliard Equation (FCHE) by considering a gradient flow in the negative order Sobolev space H−α, α ∈ [0, 1] where the choice α = 1 corresponds to the classical Cahn-Hilliard equation whilst the choice α = 0 recovers the Allen-Cahn equation. The existence of a unique solution is established and it is shown that the equation preserves mass for all positive values of fr...