International Scientific Journal

Authors of this Paper

External Links


In this paper, we have aimed the numerical inverse Laplace homotopy technique for solving some interesting 1-D time-fractional heat equations. This method is based on the Laplace homotopy perturbation method, which is combined form of the Laplace transform and the homotopy perturbation method. Firstly, we have applied to the fractional 1-D PDE by using He’s polynomials. Then we have used Laplace transform method and discussed how to solve these PDE by using Laplace homotopy perturbation method. We have declared that the proposed model is very efficient and powerful technique in finding approximate solutions to the fractional PDE.
PAPER REVISED: 2017-11-15
PAPER ACCEPTED: 2017-11-20
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Supplement 1, PAGES [S185 - S194]
  1. Kumar, D., et. al., A New Analysis for Fractional Model of Regularized Long‐Wave Equation Arising in Ion Acoustic Plasma Waves, Mathematical Methods in the Applied Sciences, (2017),
  2. Inc, M., He's Homotopy Perturbation Method for Solving Korteweg‐De Vries Burgers Equation with Initial Condition, Numerical Methods for Partial Differential Equations, 26 (2010), 5, pp. 1224-1235
  3. Özdemir, N. and Yavuz, M., Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé Approximation, Acta Physica Polonica A, 132 (2017), 3, pp. 1050-1053
  4. Yavuz, M., et. al., Generalized Differential Transform Method for Fractional Partial Differential Equation from Finance, Proceedings, International Conference on Fractional Differentiation and its Applications, Novi Sad, Serbia, 2016, pp. 778-785
  5. Yerlikaya-Özkurt, F., et. al., Estimation of the Hurst Parameter for Fractional Brownian Motion Using the Cmars Method, Journal of Computational and Applied Mathematics, 259 (2014), 843-850
  6. Kumar, S., et. al., Two Analytical Methods for Time-Fractional Nonlinear Coupled Boussinesq-Burger's Equations Arise in Propagation of Shallow Water Waves, Nonlinear Dynamics, 85 (2016), 2, pp. 699-715
  7. Ibrahim, R. W., On Holomorphic Solutions for Nonlinear Singular Fractional Differential Equations, Computers & Mathematics with Applications, 62 (2011), 3, pp. 1084-1090
  8. Özdemir, N., et. al., The Numerical Solutions of a Two-Dimensional Space-Time Riesz- Caputo Fractional Diffusion Equation, An International Journal of Optimization and Control, 1 (2011), 1, pp. 17-26
  9. Eroğlu, B. İ., et. al., Optimal Control Problem for a Conformable Fractional Heat Conduction Equation, Acta Physica Polonica A, 132 (2017), 3, pp. 658-662
  10. Evirgen, F., Conformable Fractional Gradient Based Dynamic System for Constrained Optimization Problem, Acta Physica Polonica A, 132 (2017), 3, pp. 1066-1069
  11. Hu, Y., et. al., Optimal Consumption and Portfolio in a Black-Scholes Market Driven by Fractional Brownian Motion, Infinite dimensional analysis, quantum probability and related topics, 6 (2003), 04, pp. 519-536
  12. Özdemir, N., et. al., Analysis of an Axis-Symmetric Fractional Diffusion-Wave Problem, Journal of Physics A: Mathematical and Theoretical, 42 (2009), 35, pp. 355208
  13. Jordan, H., Steady-State Heat Conduction in a Medium with Spatial Non-Singular Fading Memory: Derivation of Caputo-Fabrizio Space-Fractional Derivative from Cattaneo Concept with Jeffrey's Kernel and Analytical Solutions, Thermal Science, 21 (2017), 2, pp. 827-839
  14. Avci, D., et. al., Conformable Heat Equation on a Radial Symmetric Plate, Thermal Science, 21 (2017), 2, pp. 819-826
  15. Inc, M. and Cavlak, E., He's Homotopy Perturbation Method for Solving Coupled-Kdv Equations, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009), 3, pp. 333-340
  16. Morales-Delgado, V. F., et. al., Laplace Homotopy Analysis Method for Solving Linear Partial Differential Equations Using a Fractional Derivative with and without Kernel Singular, Advances in Difference Equations, 2016 (2016), 1, pp. 164
  17. Inc, M. and Uğurlu, Y., Numerical Simulation of the Regularized Long Wave Equation by He's Homotopy Perturbation Method, Physics Letters A, 369 (2007), 3, pp. 173-179
  18. Yavuz, M., Novel Solution Methods for Initial Boundary Value Problems of Fractional Order with Conformable Differentiation, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 8 (2017), 1, pp. 1-7
  19. Javidi, M. and Ahmad, B., Numerical Solution of Fractional Partial Differential Equations by Numerical Laplace Inversion Technique, Advances in Difference Equations, 2013 (2013), 1, pp. 375
  20. Madani, M., et. al., On the Coupling of the Homotopy Perturbation Method and Laplace Transformation, Mathematical and Computer Modelling, 53 (2011), 9, pp. 1937-1945
  21. Talbot, A., The Accurate Numerical Inversion of Laplace Transforms, IMA Journal of Applied Mathematics, 23 (1979), 1, pp. 97-120
  22. Povstenko, Y., et. al., Control of Thermal Stresses in Axissymmetric Problems of Fractional Thermoelasticity for an Infinite Cylindrical Domain, Thermal Science, 21 (2017), 1, pp. 19- 28
  23. Evirgen, F. and Özdemir, N., A Fractional Order Dynamical Trajectory Approach for Optimization Problem with Hpm, in: Fractional Dynamics and Control (Ed. D. Baleanu, J.A.T. Machado, and A.C.J. Luo), Springer, 2012, pp. 145-155
  24. Yan, L.-M., Modified Homotopy Perturbation Method Coupled with Laplace Transform for Fractional Heat Transfer and Porous Media Equations, Thermal Science, 17 (2013), 5, pp. 1409-1414
  25. Zhang, M.-F., et. al., Efficient Homotopy Perturbation Method for Fractional Non-Linear Equations Using Sumudu Transform, Thermal Science, 19 (2015), 4, pp. 1167-1171
  26. Torabi, M., et. al., Assessment of Homotopy Perturbation Method in Nonlinear Convective- Radiative Non-Fourier Conduction Heat Transfer Equation with Variable Coefficient, Thermal Science, 15 (2011), suppl. 2, pp. 263-274
  27. Hetmaniok, E., et. al., Solution of the Inverse Heat Conduction Problem with Neumann Boundary Condition by Using the Homotopy Perturbation Method, Thermal Science, 17 (2013), 3, pp. 643-650
  28. Abou-Zeid, M., Homotopy Perturbation Method to Mhd Non-Newtonian Nanofluid Flow through a Porous Medium in Eccentric Annuli with Peristalsis, Thermal Science, (2015), 00, pp. 79-79
  29. Stehfest, H., Algorithm 368: Numerical Inversion of Laplace Transforms
  30. He, J.-H., Homotopy Perturbation Technique, Computer methods in applied mechanics and engineering, 178 (1999), 3, pp. 257-262
  31. He, J.-H., Homotopy Perturbation Method for Solving Boundary Problems, Phys. Lett. A., 350 (2006), 1-2, pp. 87-88
  32. Rajabi, A., et. al., Application of Homotopy Perturbation Method in Nonlinear Heat Conduction and Convection Equations, Physics Letters A, 360 (2007), 4, pp. 570-573
  33. He, J.-H., Application of Homotopy Perturbation Method to Nonlinear Wave Equations, Chaos, Solitons & Fractals, 26 (2005), 3, pp. 695-700
  34. Odibat, Z. and Momani, S., The Variational Iteration Method: An Efficient Scheme for Handling Fractional Partial Differential Equations in Fluid Mechanics, Computers & Mathematics with Applications, 58 (2009), 11, pp. 2199-2208
  35. Chen, W., et. al., Fractional Diffusion Equations by the Kansa Method, Computers & Mathematics with Applications, 59 (2010), 5, pp. 1614-1620

© 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