Laplace transform overcoming principle drawbacks in application of the variational iteration method to fractional heat equations

Thermal Science

Volumn 16, Issue 4, 2012, Pages 1257-1261

  Wu, Guo Cheng ^a,b  

^a NEIJIANG NORMAL UNIVERSITY   (China)

^b SICHUAN UNIVERSITY   (China)

Author keywords

Fractional heat diffusion equation; Lagrange multiplier; Laplace transform; Variational iteration methods

Indexed keywords

HEAT TRANSFER; ITERATIVE METHODS; LAPLACE TRANSFORMS; PARTIAL DIFFERENTIAL EQUATIONS;

FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL HEAT DIFFUSION EQUATION; FRACTIONAL HEAT EQUATION; HEAT DIFFUSION EQUATIONS; SUCCESSIVE ITERATION; VARIATIONAL ITERATION METHOD;

LAGRANGE MULTIPLIERS;

EID: 84874535621     PISSN: 03549836     EISSN: None     Source Type: Journal    
DOI: 10.2298/TSCI1204257W     Document Type: Article

References (15)

1. 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
2. Hristov, J., Heat Balance Integral to Fractional (Half-Time) Heat Diffusion Sub-Model, Thermal Science, 14 (2010), 2, pp. 291-316
3. 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
4. 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
5. 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
6. 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
7. Podlubny, I., Fractional Differential Equations, Academic Press, New York, USA, 1999
8. Wu, G.-C., Variational Iteration Method for Solving the Time-Fractional Diffusion Equations in Porous Medium, Chin. Phys. B., 21 (2012), 12, 120504
9. Wei, M. B., Wu, G.-C., Variational Iteration Method for Sub-Diffusion Equations with the Riemann-Liouville Derivatives, Heat. Trans. Res. accepted, 2012
10. 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
11. 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
12. 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
13. 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
14. 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
15. 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