International Scientific Journal


In this article, approximate solutions of some PDE of fractional order are investi­gated with the help of a new semi-analytical method called the optimal auxiliary function method. The proposed method was tested upon the time-fractional Fisher equation, the time-fractional Fornberg-Whitham equation, and the time-fractional Inviscid Burger equation. The beauty of this method is that there is no need for discretization and assumptions of small or large parameters and provides an ap­proximate solution after only one iteration. The numerical results obtained by the proposed method compared with the other existing methods used in the literature. From the numerical and graphical results, it is clear that the proposed method gives a better solution than existing methods. The MATHEMATICA software pack­age has been used for the huge computational work.
PAPER REVISED: 2023-03-14
PAPER ACCEPTED: 2023-03-24
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Special issue 1, PAGES [9 - 17]
  1. Atangana, A., On the New Fractional Derivative and Application Non-Linear Fisher Reaction-Diffusion Equation, Applied Mathematics and Computation, 273 (2016), Jan., pp. 948-956
  2. Atangana, A., Alkahtani, B. S. T., Analysis of the Keller-Segel Model with a Fractional Derivative without Singular Kernel, Entropy, 17 (2015), 6, pp. 4439-4453
  3. Atangana, A., Baleanu, D., New Fractional Derivatives with Non-Local and Non-Singular Kernel: Theory and Application Heat Transfer Model, Thermal Science, 20 (2016), 2, pp. 763-769
  4. Ahmad, I., et al., Local Meshless Differential Quadrature Collocation Method for Time-Fractional PDE, Discrete and Continuous Dynamical Systems-S, 13 (2020), 2641
  5. Wang, F., et al., Numerical Solution of Traveling Waves in Chemical Kinetics: Time-Fractional Fishers Equations, Fractals, 30 (2022), 2, pp. 2240051-34
  6. Ahmad, H., et al., A New Analyzing Technique for Non-Linear Time Fractional Cauchy Reaction-Diffusion Model Equations, Results in Physics, 19 (2020), 103462
  7. Ahmad, I., et al., Solution of Multi-Term Time-Fractional PDE Models Arising in Mathematical Biology and Physics by Local Meshless Method, Symmetry, 12 (2020), 7, 1195
  8. Kan, M. N., et al., Numerical Solution of Time-Fractional Coupled Korteweg-de Vries and Klein-Gordon Equations by Local Meshless Method, Pramana, 95 (2021), 1, pp. 1-13
  9. Ahmad, I., et al., Application of Local Meshless Method for the Solution of Two Term Time Fractional-Order Multi-Dimensional PDE Arising in Heat and Mass Transfer, Thermal Science, 24 (2020), Suppl. 1, pp. S95-S105
  10. Srivastava, M. H., et al., Numerical Simulation of 3-D Fractional-Order Convection-Diffusion PDE by a Local Meshless Method, Thermal Science, 25 (2020), 1A, pp. 347-358
  11. Shakeel, M., et al., Meshless Technique for the Solution of Time-Fractional Partial Differential Equations Having Real-World Applications, Journal Funct. Spaces, 2020 (2020), ID8898309
  12. Marinca, B., Marinca, V., Approximate Analytical Solutions for Thin Film Flow of a Fourth Grade Fluid Down a Vertical Cylinder, Proceed Romanian Academy, Series A, 19 (2018), 1, pp. 69-76
  13. Marinca, V., Herisanu, N., An Application of the Optimal Auxiliary Functions to Blasius Problem, The Romanian Journal of Technical Sciences, Applied Mechanics, 60 (2015), 3, pp. 206-215
  14. Zada, L., et al., New Algorithm for the Approximate Solution of Generalized Seventh Order Korteweg-Devries Equation Arising in Shallow Water Waves, Results in Physics, 20 (2021), 103744
  15. Singh, P., Sharma, D., Comparative Study of Homotopy Perturbation Transformation with Homotopy Perturbation Elzaki Transform Method for Solving Non-Linear Fractional PDE, Non-Linear Engineering, 9 (2020), 1, pp. 60-71

© 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