International Scientific Journal

Authors of this Paper

External Links


In this paper, the Adomian decomposition method and the fractional complex transform are adopted to solve a fractional Bratu-type equations based on He's fractional derivative. The solution process is elucidated and analytical results can be directly used in practical applications.
PAPER REVISED: 2016-08-23
PAPER ACCEPTED: 2016-10-25
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Issue 4, PAGES [1713 - 1717]
  1. He, J.-H., et al., Variational Iteration Method for Bratu-Like Equation Arising in Electrospinning, Car-bohydrate Polymers, 105 (2013), May, pp. 229-230
  2. He, J.-H., Liu, H. M., Variational Approach to Nonlinear Problems and a Review on Mathematical Model of Electrospinning, Nonlinear Analysis-Theory Methods & Applications, 63 (2005), 5-7, pp. 919-929
  3. Wan, Y. Q., et al., Thermo-Electro-Hydrodynamic Model for Electrospinning Process, Int. J. Nonlinear Sci. Numer., 5 (2004), 1, pp. 5-8
  4. Liu, H. Y., Wang, P., A Short Remark on WAN Model for Electrospinning and Bubble Electrospinning and Its Development, Int. J. Nonlinear Sci. Numer., 16 (2015), 1, pp. 1-2
  5. Colantoni, A., Boubaker, K., Electro-Spun Organic Nanofibers Elaboration Process Investigations Using Comparative Analytical Solutions, Carbohydrate Polymers, 101 (2014), Jan., pp. 307-312
  6. Podlubny, I., Fractional Differential Equations, Academic Press, New York, USA, 1999
  7. Hilfer, R., Application of Fractional Calculus in Physics, World Scientific, Singapore, 2000
  8. Hu, Y., He, J.-H., On Fractal Space-Time and Fractional Calculus, Thermal Science, 20 (2016), 3, pp. 773-777
  9. Wang, K. J., Pan, Z. L, An Analytical Model for Steady-State and Transient Temperature Fields in 3-D Integrated Circuits, IEEE Trans. Compon., Packag., Manuf. Technol., 6 (2016), 7, pp. 1028-1041
  10. Wang, K. J., et al., Integrated Microchannel Cooling in a Three Dimensional Integrated Circuit: A Thermal Management, Thermal Science, 20 (2016), 3, pp. 899-902
  11. He, J.-H., Homotopy Perturbation Technique, Computer Methods in Applied Mechanics and Engineer-ing, 178 (1999), 3, pp. 257-262
  12. He, J.-H., A Coupling Method of a Homotopy Technique and a Perturbation Technique for Nonlinear Problems, International Journal of Nonlinear Mechanics, 35 (2000), 1, pp. 37-43
  13. He, J.-H., Application of Homotopy Perturbation Method to Nonlinear Wave Equation, Chaos, Solitons & Fractals, 26 (2005), 3, pp. 695-700
  14. Rajeev., Homotopy Perturbation Method for a Stefan Problem with Variable Latent Heat, Thermal Sci-ence, 18 (2014), 2, pp. 391-398
  15. He, J.-H., A Short Remark on Fractional Variational Iteration Method, Phys. Lett. A 375 (2011), 38, pp. 3362-3364
  16. He, J.-H., Variational Iteration Method - Some Recent Results and New Interpretations, J. Comput. Appl. Math., 207 (2007), 1, pp. 3-17
  17. He, J.-H., Exp-Function Method for Fractional Differential Equations, International Journal of Nonline-ar Sciences and Numerical Simulations, 14 (2013), 6, pp. 363-366
  18. Ma, H. C., et al., Exact Solutions of Nonlinear Fractional Partial Differential Equations by Fractional Sub-Equation Method, Thermal Science, 19 (2015), 4, pp. 1239-1244
  19. Wazwaz, A. M., A Reliable Modification of Adomian Decomposition Method, Appl. Math. Comput., 102 (1999), 1, pp. 77-86
  20. Adomian, G., A Review of the Decomposition Method in Applied Mathematics, J. Math. Anal. Appl., 135 (1988), 2, pp. 501-504
  21. He, J.-H., Li, Z. B., Converting Fractional Differential Equations into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334
  22. Li, Z., He, J.-H., Fractional Complex Transform for Fractional Differential Equations, Math. Comput. Appl., 15 (2010), 5, pp. 970-973
  23. Wazwaz, A. M., Adomian Decomposition Method for a Reliable Treatment of the Bratu-Type Equa-tions, Appl. Math. Comput., 166 (2005), 3, pp. 652-663
  24. He, J.-H., et al., A New Fractional Derivative and Its Application to Explanation of Polar Bear Hairs, Journal of King Saud University Science, 28 (2015), 2, pp. 190-192
  25. He, J.-H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, Int. J. Theor. Phys., 53 (2014), 11, pp. 3698-3718

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, 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