FRACTIONAL MODEL FOR HEAT CONDUCTION IN POLAR BEAR HAIRS

Abstract

Time-fractional differential equations can accurately describe heat conduction in fractal media, such as wool fibers, goose down and polar bear hair. The fractional complex transform is used to convert time-fractional heat conduction equations with the modified Riemann-Liouville derivative into ordinary differential equations, and exact solutions can be easily obtained. The solution process is straightforward and concise.

Keywords

Dates

  • Submission Date2011-05-03
  • Revision Date2011-07-11
  • Acceptance Date2011-07-18

DOI Reference

10.2298/TSCI110503070W

References

  1. J. Hristov, Approximate solutions to fractional subdiffusion equations, European Physical Journal, 193(2011), 1, pp. 229-243
  2. J. Hristov, Starting radial subdiffusion from a central point through a diverging medium (A sphere): Heat-Balance Integral Method, Thermal Science, 15(2011),s, pp. S5-S20
  3. J. Hristov, Heat-balance integral to fractional (half-time) heat diffusion sub-model, Thermal Science, 14(2010), 2, pp. 291-316
  4. Wu, G.C., A Fractional Lie Group Method for Anomalous Diffusion Equations, Communications in Fractional Calculus, 1(2010), 1, pp. 27-31
  5. 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
  6. Jafari, H., Kadkhoda, N., Tajadodi, H., et al. Homotopy Perturbation Pade Technique for Solving Fractional Riccati Differential Equations, Int. J. Nonlinear Sci. Num., 11(2010), s, pp. 271-275
  7. 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
  8. Rida, S.Z., El-Sayed, A.M.A., Arafa, A.A.M., A Fractional Model for Bacterial Chemoattractant in a Liquid Medium, Nonlinear Science Letters A, 1(2010),4, pp. 419-424
  9. Zhang, S., Zong, Q.-A., Liu, D., Gao, Q., A Generalized Exp-Function Method for Fractional Riccati Differential Equations, Communications in Fractional Calculus, 1(2010), 1, pp. 48-51
  10. He, J.H., A New Fractal Derivation, Thermal Science, 15(2011), s, pp. S145-S147
  11. He J.H., Analytical methods for thermal science-An elementary introduction, Thermal Science, 15(2011), s, pp. S1-S3
  12. Li, Z.B., He, J.H., Fractional Complex Transform for Fractional Differential Equations, Mathematical and Computational Applications, 15(2010), 5, pp. 970-973
  13. Li, Z.B., An Extended Fractional Complex Transform, Journal of Nonlinear Science and Numerical Simulation, 11(2010), s, pp. 0335-0337.
  14. Wang, Q.-L., He, J.-H., Pan, N., Structure of Polar Bear Hair, Nonlinear Science Letters D, 1(2010), pp. 159-162
  15. Jumarie, G., Cauchy's integral formula via the modified Riemann-Liouville derivative for analytic functions of fractional order, Applied Mathematics Letters, 23(2010), 12, pp. 1444-1450
  16. Jumarie, G., Fractional partial differential equations and modified Riemann- Liouville derivative new methods for solution, Journal of Applied Mathematics and Computing, 24(2007), 1-2, pp. 31-48
  17. Jumarie, G., modified Riemann-Liouville Derivative and Fractional Taylor series of Non-differentiable Functions Further Results, Computers and Mathematics with Applications, 51 (2006), 9-10, pp. 1367-1376
  18. He, J.H., Wang, Q. L., Sun, J., Can polar bear absorb environmental energy? Thermal Science, 16(2011), 3, pp.xxx-xxx
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