## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### An operational matrix for solving time-fractional order Cahn-Hilliard equation

**ABSTRACT**

In the present scientific work, an operational matrix scheme with Laguerre polynomials is applied to solve a space-time fractional order non-linear Cahn-Hilliard equation, which is used to calculate chemical potential and free energy for a non-homogeneous mixture. Constructing operational matrix for fractional differentiation, the collocation method is applied to convert Cahn-Hilliard equation into an algebraic system of equations, which have been solved using Newton method. The prominent features of the manuscript is to providing the stability analysis of the proposed scheme and the pictorial presentations of numerical solution of the concerned equation for different particular cases and showcasing of the effect of advection and reaction terms on the nature of solute concentration of the considered mathematical model for different particular cases.

**KEYWORDS**

PAPER SUBMITTED: 2019-07-25

PAPER REVISED: 2019-08-30

PAPER ACCEPTED: 2019-09-03

PUBLISHED ONLINE: 2019-10-06

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