## THERMAL SCIENCE

International Scientific Journal

### VARIABLE SEPARATION FOR TIME FRACTIONAL ADVECTION-DISPERSION EQUATION WITH INITIAL AND BOUNDARY CONDITIONS

**ABSTRACT**

In this paper, variable separation method combined with the properties of Mittag-Leffler function is used to solve a variable-coefficient time fractional advection-dispersion equation with initial and boundary conditions. As a result, a explicit exact solution is obtained. It is shown that the variable separation method can provide a useful mathematical tool for solving the time fractional heat transfer equations.

**KEYWORDS**

PAPER SUBMITTED: 2015-11-28

PAPER REVISED: 2015-12-18

PAPER ACCEPTED: 2016-02-02

PUBLISHED ONLINE: 2016-08-13

**THERMAL SCIENCE** YEAR

**2016**, VOLUME

**20**, ISSUE

**3**, PAGES [789 - 792]

- Parvizi, M., et al., Numerical Solution of Fractional Advection-Diffusion Equation with a Non-Linear Source Term, Numerical Algorithms, 68 (2015), 3, pp. 601-629
- Khan, H., et al., Existence and Uniqueness Results for Coupled System of Fractional q-Diffe ence Equations with Boundary Conditions, Journal of Computational Complexity and Applications, 1 (2015), 2, pp. 79-88
- Yang, X. J., et al., Fractal Boundary Value Problems for Integral and Differential with Local Fractional Operators, Thermal Science, 19 (2015), 3, pp. 959-966
- Das, S., Kumar, R., Fractional Diffusion Equations in the Presence of Reaction Terms, Journal of Computational Complexity and Applications, 1 (2015), 1, pp. 15-21
- Wu, G. C., et al., Lattice Fractional Diffusion Equation in Terms of a Riesz-Caputa Difference, Physica A, 438 (2015), 1, pp. 283-287
- Huang, F., et al., The Fundamental Solution of the Space-Time Frac tional Advection-Dispersion Equation, Journal of Computational and Applied Mathematics, 18 (2005), 1-2, pp. 339-350
- El-Sayed, A. M. A., et al., Adomian's Decomposi ion Method for Solving an Intermediate Fractional Advection-Dispersion Equation, Computers & Mathematics with Applications, 59 (2010), 5, pp. 1759-1765
- Golbabai, A., Sayevand, K., Analytical Modelling of Fractional Advection-Dispersion Equation Defined in a Bounded Space Domain, Mathematical & Com puter Modelling, 53 (2011), 9-10, pp. 1708-1718
- He, J.-H., Variational Iteration Method? Some Recent Results and New Interpretations, Journal of Computational and Applied Mathematics, 207 (2013), 1, pp. 3-17
- Cui, L. X., et al., New Exact Solutions of Fractional Hirota-Satsuma Coupled Korteweg-de Vries Equations, Thermal Science, 19 (2015), 4, pp. 1173-1176
- Liu, Y., et al., Multi-Soliton Solutions of the Forced Variable-Coefficient Extended Korteweg-de Vries Equation Arisen in Fluid Dynamics of Internal Solitary Waves, NonLinear Dynamics, 66 (2011), 4, pp. 575-587
- Zhang, S., et al., Variable Separation Method for Non-Linear Time Fractional Biological Population Model, International Journal of Numerical Methods for Heat & Fluid Flow, 25 (2015), 7, pp. 1531-1541
- Secer, A., Approximate Analytic Solution of Fractional Heat-Like and Wave-Like Equations with Variable Coefficients Using the Differential Transform Method, Advances in Difference Equations, 2012 (2012), 1, p. 198