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May 4, 2023
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Abstract

In this paper, we obtain the exact solutions of fractional differential equation with Atangana-Baleanu fractional derivative (ABFD) by using fractional Adomian decomposition method (FADM). The exact solutions of PDEs with fractional order are successfully obtained using the proposed method.

Keywords

Atangana-Baleanu FADM

Article Details

How to Cite
Zayir, M. Y. (2023). THE EXACT SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 4(5), 1-8. https://doi.org/10.17605/OSF.IO/7XS5Y

References

  1. 1. S. Q. Wang, Y. J. Yang, and H. K. Jassim, Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative, Abstract and Applied Analysis, 2014 (2014) 1-7: ID 176395.
  2. 2. S. P. Yan, H. Jafari, and H. K. Jassim, Local Fractional Adomian Decomposition and Function Decomposition Methods for Solving Laplace Equation within Local Fractional Operators, Advances in Mathematical Physics, 2014 (2014) 1-7: ID 161580.
  3. 3. H. K. Jassim, C. Ünlü, S. P. Moshokoa, C. M. Khalique, Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators, Mathematical Problems in Engineering, 2015 (2015) 1-9: ID 309870.
  4. 4. Z. P. Fan, H. K. Jassim, R. K. Rainna, and X. J. Yang, Adomian Decomposition Method for Three-Dimensional Diffusion Model in Fractal Heat Transfer Involving Local Fractional Derivatives, Thermal Science, 19(2015) S137-S141.
  5. 5. S. Xu, X. Ling, Y. Zhao, H. K. Jassim, A Novel Schedule for Solving the Two-Dimensional Diffusion in Fractal Heat Transfer, Thermal Science, 19 (2015) S99-S103.
  6. 6. H. Jafari, H. K. Jassim, and S. T. Mohyuid-Din, Local Fractional Laplace Decomposition Method for Solving Linear Partial Differential Equations with Local Fractional Derivative. In Fractional Dynamics. C. Cattani, H. M. Srivastava, and X.-J. Yang (Editors), De Gruyter Open, Berlin and Warsaw (2015) 296-316.
  7. 7. H. K. Jassim, New Approaches for Solving Fokker Planck Equation on Cantor Sets within Local Fractional Operators, Journal of Mathematics, 2015(2015)1-8 :ID 684598.
  8. 8. H. Jafari, H. K. Jassim, S. P. Moshokoa, V. M. Ariyan and F. Tchier, Reduced differential transform method for partial differential equations within local fractional derivative operators, Advances in Mechanical Engineering, 8(4) (2016) 1-6.
  9. 9. H. Jafari, H. K. Jassim, F. Tchier, D. Baleanu, On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operator, Entropy, 18 (2016) 1-12.
  10. 10. D. Baleanu, H. K. Jassim, Approximate Analytical Solutions of Goursat Problem within Local Fractional Operators, Journal of Nonlinear Science and Applications, 9(2016) 4829-4837.
  11. 11. H. K. Jassim, The Approximate Solutions of Three-Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operator, Abstract and Applied Analysis, 2016 (2016) 1-5: ID 2913539.
  12. 12. H. Jafari, H. K. Jassim, On the Existence and Uniqueness of Solutions for Local differential equations, Entropy, 18(2016) 1-9.
  13. 13. D. Baleanu, H. K. Jassim, H. Khan, A Modification Fractional Variational Iteration Method for solving Nonlinear Gas Dynamic and Coupled KdV Equations Involving Local Fractional Operators, Thermal Science, 22( 2018) S165-S175.
  14. 14. H. Jafari, H. K. Jassim, J. Vahidi, Reduced Differential Transform and Variational Iteration Methods for 3D Diffusion Model in Fractal Heat Transfer within Local Fractional Operators, Thermal Science, 22( 2018) S301-S307.
  15. 15. H. K. Jassim, W. A. Shahab, Fractional variational iteration method to solve one dimensional second order hyperbolic telegraph equations, Journal of Physics: Conference Series, 1032(1) (2018) 1-9.
  16. 16. H. K. Jassim, D. Baleanu, A novel approach for Korteweg-de Vries equation of fractional order, Journal of Applied Computational Mechanics, 5(2) (2019) 192-198.
  17. 17. D. Baleanu, H. K. Jassim, Approximate Solutions of the Damped Wave Equation and Dissipative Wave Equation in Fractal Strings, Fractal and Fractional, 3(26) (2019) 1-12.
  18. 18. D. Baleanu, H. K. Jassim, A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets, Fractal and Fractional, 3(30) (2019) 1-8.
  19. 19. D. Baleanu, H. K. Jassim, M. Al Qurashi, Solving Helmholtz Equation with Local Fractional Derivative Operators, Fractal and Fractional, 3(43) (2019) 1-13.
  20. 20. H. K. Jassim, Analytical Approximate Solutions for Local Fractional Wave Equations, Mathematical Methods in the Applied Sciences, 43(2) (2020) 939-947.
  21. 21. J. Singh, H. K. Jassim, D. Kumar, An efficient computational technique for local fractional Fokker-Planck equation, Physica A: Statistical Mechanics and its Applications, 555(124525) (2020) 1-8.
  22. 22. H. K. Jassim, J. Vahidi, V. M. Ariyan, Solving Laplace Equation within Local Fractional Operators by Using Local Fractional Differential Transform and Laplace Variational Iteration Methods, Nonlinear Dynamics and Systems Theory, 20(4) (2020) 388-396.
  23. 23. D. Baleanu, H. K. Jassim, Exact Solution of Two-dimensional Fractional Partial Differential Equations, Fractal Fractional, 4(21) (2020) 1-9.
  24. 24. H. K. Jassim, M. G. Mohammed, H. A. Eaued, A Modification Fractional Homotopy Analysis Method for Solving Partial Differential Equations Arising in Mathematical Physics, IOP Conf. Series: Materials Science and Engineering, 928 (042021) (2020) 1-22.
  25. 25. H. A. Eaued, H. K. Jassim, M. G. Mohammed, A Novel Method for the Analytical Solution of Partial Differential Equations Arising in Mathematical Physics, IOP Conf. Series: Materials Science and Engineering, 928 (042037 ) (2020) 1-16.
  26. 26. H. K. Jassim, J. Vahidi, A New Technique of Reduce Differential Transform Method to Solve Local Fractional PDEs in Mathematical Physics, International Journal of Nonlinear Analysis and Applications, 12(1) (2021) 37-44.
  27. 27. S. M. Kadhim, M. G. Mohammad, H. K. Jassim, How to Obtain Lie Point Symmetries of PDEs, Journal of Mathematics and Computer science, 22 (2021) 306-324.
  28. 28. H. K. Jassim, M. A. Shareef, On approximate solutions for fractional system of differential equations with Caputo-Fabrizio fractional operator, Journal of Mathematics and Computer science, 23 (2021) 58-66.
  29. 29. H. K. Jassim, S. A. Khafif, SVIM for solving Burger’s and coupled Burger’s equations of fractional order, Progress in Fractional Differentiation and Applications, 7(1) (2021)1-6.
  30. 30. H. K. Jassim, H. A. Kadhim, Fractional Sumudu decomposition method for solving PDEs of fractional order, Journal of Applied and Computational Mechanics, 7(1) (2021) 302-311.
  31. 31. H. Jafari, H. K. Jassim, D. Baleanu, Y. M. Chu, On the approximate solutions for a system of coupled Korteweg-de Vries equations with local fractional derivative, Fractals, 29(5)(2021) 1-7.
  32. 32. H. K. Jassim, M. G. Mohammed, Natural homotopy perturbation method for solvingnonlinear fractional gas dynamics equations, International Journal of Nonlinear Analysis and Applications, 12(1) (2021) 813-821.
  33. 33. M. G. Mohammed, H. K. Jassim, Numerical simulation of arterial pulse propagation using autonomous models, International Journal of Nonlinear Analysis and Applications, 12(1) (2021) 841-849.
  34. 34. H. K. Jassim, A new approach to find approximate solutions of Burger’s and coupled Burger’s equations of fractional order, TWMS Journal of Applied and Engineering Mathematics, 11(2) (2021) 415-423.
  35. 35. L. K. Alzaki, H. K. Jassim, The approximate analytical solutions of nonlinear fractional ordinary differential equations, International Journal of Nonlinear Analysis and Applications, 12(2) (2021) 527-535.
  36. 36. E. K. Amer, N. J. Hassan, H. K. Jassim, Non-Bayesian estimation of Weibull Lindley burr XII distribution, , International Journal of Nonlinear Analysis and Applications, 12(2) (2021) 977-989.
  37. 37. H.K. Jassim, H. Ahmad, A. Shamaoon, C. Cesarano, An efficient hybrid technique for the solution of fractional-order partial differential equations, Carpathian Mathematical Publications, 13(3) (2021) 790-804.
  38. 38. H. G. Taher, H. Ahmad, J. Singh, D. Kumar, H. K. Jassim, Solving fractional PDEs by using Daftardar-Jafari method, AIP Conference Proceedings, 2386(060002) (2022) 1-10.
  39. 39. A. H. Mktof, N. J. Hassan, H. K. Jassim, Weibull Lindley Pareto distribution, AIP Conference Proceedings, 2386(060015) (2022) 1-11.
  40. 40. L. K. Alzaki, H. K. Jassim, Time-Fractional Differential Equations with an Approximate Solution, Journal of the Nigerian Society of Physical Sciences, 4 (3)(2022) 1-8.