International Scientific Journal

Thermal Science - Online First

online first only

Adomian-Padé approximate solutions to the conformable nonlinear heat transfer equation

This paper adopts the Adomian decomposition method and the Padé approximation technique to derive the approximate solutions of a conformable heat transfer equation by considering the new definition of the Adomian polynomials (APs). The Padé approximate solutions are derived along with interesting figures showing the approximate solutions.
PAPER REVISED: 2018-11-20
PAPER ACCEPTED: 2019-01-11
  1. Whitham, G.B., Linear and Nonlinear Waves, John Wiley, New York, 1974
  2. Ferziger, J.H., A note on numerical accuracy, Int. J. Num. M. in fluids, 8 (1988), pp. 995-996
  3. Podlubny, I., Fractional Differential Equations, Academic Press, New York, USA, 1999
  4. Yang, X.J., Advanced Local Fractional Calculus and its Applications, World Science Publisher, New York, USA, 2012
  5. Khalil . R., et al., A new definition of fractional derivativ, J. Comput. Appl. Mat., 264 (2014), pp. 65-70
  6. Wang, K.L. and Liu, Y., He's fractional derivative for nonlinear fractional heat transfer equation, Thermal Science, 20 (2016), pp. 793-796
  7. Zhang. M. F., Liu, Y.Q., Zhou, X.Z., Efficient homotopy perturbation method for fractional nonlinear equations using Sumudu transform, Thermal Science, 19 (2015), pp. 1167-1171
  8. Ma . H.C., et al., Exact solutions of nonlinear fractional partial differential equations by fractional sub-equation method, Thermal Science, 19 (2015), pp.1239-1244
  9. Lin. Y., et al., Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations, Computer Physics Communications, 184 (2013), pp.130-141
  10. Rach. R., A new definition of the Adomian polynomials, Kybernetes, 37 (2008), pp. 910-955
  11. Hosseini M., et al., On the convergence of Adomian decomposition method, Applied Mathematics and Computation, 182 (2006), pp. 536-543
  12. Wu. G., Adomian decomposition method for non-smooth initial value problems, Mathematical and Computer Modelling, 54 (2011), pp. 2104-2108
  13. Qin. Z., et al., Analytic study of solitons in non-kerr nonlinear negative index materials, Nonlinear Dynamics, 86 (2016), pp. 623-638
  14. Mirzazadeh. M, et al., Optical solitons with complex Ginzburg-Landau equation, Nonlinear Dynamics, 85 (2016), pp. 1979-2016
  15. Bo. L., et al., Soliton interactions for optical switching systems with symbolic computations, Optik, 175 (2018), pp.177-180
  16. Zubair. A., et al., Analytic study on optical solitons in parity-time-symmetric mixed linear and nonlinear modulation lattices with non-Kerr nonlinearities, Optik, 173 (2018), pp. 249-262
  17. Weitian. Y., et al., Periodic oscillations of dark solitons in nonlinear optics, Optik, 165 (2018), pp. 341-344
  18. Zhou, Q., et al., Optical solitons in media with time-modulated nonlinearities and spatiotemporal dispersion, Nonlinear Dynamics, 80 (2015), pp. 983-987
  19. Zhou, Q., Optical solitons for Biswas-Milovic model with Kerr law and parabolic law nonlinearities, Nonlinear Dynamics, 84 (2016), pp. 677-681
  20. Triki, H., et al., Chirped dark solitons in optical metametarials, Optik, 158 (2018), pp. 312-315