## THERMAL SCIENCE

International Scientific Journal

### LAPLACE TRANSFORM OVERCOMING PRINCIPLE DRAWBACKS IN APPLICATION OF THE VARIATIONAL ITERATION METHOD TO FRACTIONAL HEAT EQUATIONS

**ABSTRACT**

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 successive iterations.

**KEYWORDS**

PAPER SUBMITTED: 2012-10-19

PAPER ACCEPTED: 2012-10-23

**THERMAL SCIENCE** YEAR

**2012**, VOLUME

**16**, ISSUE

**Issue 4**, PAGES [1257 - 1261]

- Meilanov, R., Shabanova, M., Akhmedov, E., AResearch Note on a Solution of Stefan Problem with Fractional Time and Space Derivatives, Int. Rev. Chem. Eng., 3 (2011), 6, pp. 810-813
- Hristov, J., Heat Balance Integral to Fractional (Half-Time) Heat Diffusion Sub-Model, Thermal Science, 14 (2010), 2, pp. 291-316
- Siddique, I., Vieru, D., Stokes Flows of a Newtonian Fluid with Fractional Derivatives and Slip at the Wall, Int. Rev. Chem. Eng., 3 (2011), 6, pp. 822- 826
- Qi , H., Xu, M., Some Unsteady Unidirectional Flows of a Generalized Oldroyd-B Fluid with Fractional Derivative, Appl. Math. Model., 33 (2009), 11, pp. 4184-4191
- He, J.-H., Approximate Analytical Solution for Seepage Flow with Fractional Derivatives in Porous Media, Comput. Method. Appl. M., 167 (1998), 1-2, pp. 57-68
- He, J.-H., Variational Iteration Method - a Kind of Non-Linear Analytical Technique: Some Examples, Int. J. Nonlinear Mech., 34 (1999), 4, pp. 699-708
- Podlubny, I., Fractional Differential Equations, Academic Press, New York, USA, 1999
- Wu, G.-C., Variational Iteration Method for Solving the Time-Fractional Diffusion Equations in Porous Medium, Chin. Phys. B., 21 (2012), 12, 120504
- Wei, M. B., Wu, G.-C., Variational Iteration Method for Sub-Diffusion Equations with the Riemann-Liouville Derivatives, Heat. Trans. Res. accepted, 2012
- Wu, G.-C., Applications of the Variational Iteration Method to Fractional Diffusion Equations: Local Versus Nonlocal Ones, Int. Rev. Chem. Eng., 4 (2012), 5, pp. 505-510
- Momani, S., Odibat, Z., Analytical Approach to Linear Fractional Partial Differential Equations Arising in Fluid Mechanics, Phys. Lett., A 355 (2006), 4-5, pp. 271-279
- Inc, M., The Approximate and Exact Solutions of the Space- and Time-Fractional Burgers Equations with Initial Conditions by Variational Iteration Method, J. Math. Anal. Appl., 345 (2008), 1, pp. 476-484
- Molliq, R. Y., Noorani, M. S. M., Hashim, I., Variational Iteration Method for Fractional Heat- and Wave-Like Equations, Nonlinear Analysis: Real World Applications, 10 (2009), 3, pp. 1854-1869
- Sakar, M. G., Erdogan, F., Yildirim, A., Variational Iteration Method for the Time-Fractional Fornberg-Whitham Equation, Comput. Math. Appl., 63 (2012), 9, pp. 1382-1388
- Hristov, J., An Exercise with the He's Variation Iteration Method to a Fractional Bernoulli Equation Arising in Transient Conduction with Non-Linear Heat Flux at the Boundary, Int. Rev. Chem. Eng., 4 (2012), 5, pp. 489-497