International Scientific Journal

Authors of this Paper

External Links


Efficient finite-difference scheme to solve fractional diffusion-wave equations without initial conditions has been developed. The efficient approximation of the Riesz fractional derivatives is demonstrated and efficiently exemplified by two simple problems with/without source terms.
PAPER REVISED: 2012-05-02
PAPER ACCEPTED: 2012-08-25
CITATION EXPORT: view in browser or download as text file
  1. Oldham , K.B., J. Spanier ,J., The Fractional calculus , Academic Press, New York, 1974.
  2. I. Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, 1999.
  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. Hristov, J., Transient Flow of A Generalized Second Grade Fluid Due to a Constant Surface Shear Stress: an approximate Integral-Balance Solution , Int. Rev. Chem. Eng., 3 (2011), 6, pp. 802-809.
  6. Agrawal , O.P., Application of Fractional Derivatives in Thermal Analysis of Disk Brakes , Nonlinear Dynamics , 38( 2004),1, pp. 191-206.
  7. Hristov, J., Heat-Balance Integral to Fractional (Half-Time) Heat Diffusion Sub-Model, Thermal Science, 14 (2) (2010), 2, pp. 291-316. DOI: 10.2298/TSCI1002291H
  8. Kulish , V.V., Lage, J.L., Fractional-diffusion solutions for transient local temperature and heat flux, J. Heat Transfer, 122 (2000),2,pp.372-376.
  9. dos Santos, M.C., Lenzi, E., Gomes, E.M., Lenzi,, M.K., Lenzi, E.K., Development of Heavy Metal sorption Isotherm Using Fractional Calculus, Int. Rev. Chem. Eng., 3 (2011),6,pp. 814-817.
  10. Hristov, J., Starting radial subdiffusion from a central point through a diverging medium (a sphere): Heat-balance Integral Method, Thermal Science, 15 (2011), S1, pp. S5-S20 .
  11. Voller, V.R., An exact solution of a limit case Stefan problem governed by a fractional diffusion equation, Int. J. Heat Mass Transfer, 53 (2010),23-24, pp. 5622-5625.
  12. Pfaffenzeller, R.A., Lenzi,M.K., Lenzi, E.K., Modeling of Granular Material Mixing Using Fractional Calculus, Int. Rev. Chem. Eng., 3 (2011),6,pp. 818-821.
  13. Meilanov , R.P., Shabanova, M.R., Akhmedov, E.N., A Research Note on a Solution of Stefan Problem with Fractional Time and Space Derivatives, Int. Rev. Chem. Eng., 3 (2011),6, pp. 810-813.
  14. Liu, J., Xu, M., Some exact solutions to Stefan problems with fractional differential equations, J. Math. Anal. Appl., 351(2010),2, pp.536-542
  15. Jafari,H. Kadkhoda,N., Tajadodi, al. , Homotopy Perturbation Pade Technique for Solving Fractional Riccati Differential Equations, Int. J. Nonlinear Sci. Num., 11(2010),s, pp. 271-275. DOI: 10.1515/IJNSNS.2010.11.S1.271
  16. Golbabai A., Sayevand,K., The Homotopy Perturbation Method for Multi-order Time Fractional Differential Equations, Nonlinear Science Letters A, 1(2010), 2, pp.147-154
  17. He, J. H., Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer Methods in Applied Mechanics and Engineering, 167(1998), 1-2, pp. 57-68
  18. Hristov, J., Approximate solutions to fractional subdiffusion equations, European Physical Journal, 193(2011), 1, pp. 229-243
  19. Hristov, J., A Short-Distance Integral-Balance Solution to a Strong Subdiffusion Equation: A Weak Power-Law Profile, Int. Rev. Chem. Eng..,5(2) (2010),5, pp. 555-563
  20. Zhang, S., Zhang, H.Q., Fractional sub-equation method and its applications to nonlinear fractional PDEs, Physics Letters A, 375(2011), 7, pp. 1069-1073
  21. He J.H., Analytical methods for thermal science-An elementary introduction, Thermal Science, 15(2011), s, pp. S1-S3
  22. He, J.H., A New Fractal Derivation, Thermal Science, 15(2011), s, pp. S145-S147
  23. Meerschaert,M.M., Tadjeran, C., Finite difference approximations for fractional advection-dispersion flow equations, J. Comput. Appl. Math. 172(2004), 1, pp.65-77.
  24. Lynch V.E., Carreras B.A., del-Castill-Negrete D., Ferreira-Mejias K.M., Hicks H.R. Numerical methods for the solution of partial differential equations of fractional order. J. Comp. Phys. , 192 (2003),2, pp. 406-421.
  25. Beibalaev, B.D.Б., Mathematical model of transport on media with fractal structures, Mathematical Modelling, 21(2009),5, pp.55-62 (in Russian)
  26. Garg M., Manohar P. , Numerical solution of fractional diffusion-wave equation with two space variables by matrix method, Fractional Calculus and Applied Analysis , 13 (2005), 2, pp. 191-207.
  27. Katsikadelis J.T., The BEM for numerical solution of partial fractional differential equations, Computers & Mathematics with Applications, 62 (2011),3, pp.891-901. doi:10.1016/j.camwa.2011.04.001.
  28. Liu, J., Hou, G., Numerical solutions of the space- and time-fractional coupled Burgers equations by generalized differential transform method, Applied Mathematics and Computation, 217 (2011), 16,pp. 7001-7008, doi:10.1016/j.amc.2011.01.111
  29. Li C., Zhao Z, Chen Y-Q., Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion, Computers & Mathematics with Applications, 62 (2011),3, pp.855-875. doi:10.1016/j.camwa.2011.02.045.
  30. Odibat, Z.M., Rectangular decomposition method for fractional diffusion-wave equations, Applied Mathematics and Computation, 179 (2006),1, pp. 92-97.

© 2020 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence