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The homotopy analysis Rangaig transform method for nonlinear partial differential equations

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The idea suggested in this article is to combine the Rangaig transform with the homotopy analysis method in order to facilitate the solution of nonlinear partial differentia equations. This method may be called the homotopy analysis Rangaig transform method (HARTM). The proposed example results showed that HARTM is an effective method for solving nonlinear partial differential equations.
Rocznik
Strony
111--122
Opis fizyczny
Bibliogr. 30 poz., tab.
Twórcy
  • Faculty of Exact Sciences and Informatics, Pole of Ouled Fares, Hassiba Benbouali University of Chlef, Algeria
  • Preparatory Cycle Department, Oran’s Hight School of Electrical and Energetics Engineering (ESGEE-Oran), Oran, Algeria
Bibliografia
  • [1] Abd El Salam, M.A., Ramadan, M.A., Nassar, M.A., Agarwal, P., & Chu, Y.M. (2021). Matrix computational collocation approach based on rational Chebyshev functions for nonlinear differential equations. Advances in Difference Equations, 331, 1-17.
  • [2] Ahmad, H., Akgul, A., Khan, T.A., Stanimirovi ̆c, P.S., & Chu, Y.M. (2020). New perspective on the conventional solutions of the nonlinear time-fractional partial differential equations. Complexity, 2020, Article ID 8829017, 1-10.
  • [3] Ejaz, S.T, Mustafa, G., Baleanu, D., & BChu, Y.M. (2021). The refinement-schemes-based unified algorithms for certain nth order linear and nonlinear differential equations with a set of constraints. Advances in Difference Equations, 121, 1-16.
  • [4] Karthikeyan, K., Karthikeyan, P., Baskonus, H.M, Venkatachalam, K., & Chu, Y.M. (2021). Almost sectorial operators on Ψ-Hilfer derivative fractional impulsive integro-differential equations. Mathematical Methods in the Applied Sciences, 1-15.
  • [5] Khan, A., Farooq, M., Nawaz, R., Ayaz, M., Ahmad, H., Abu-Zinadah, H., & Chu, Y.M. (2021). Analysis of couple stress fluid flow with variable viscosity using two homotopy-based methods. Open Physics, 19, 134–145.
  • [6] Farooq, M., Khan, A., Nawaz, R., Islam, S., Ayaz, M., & Chu, Y.M. (2021). Comparative study of generalized couette flow of couple stress fluid using optimal homotopy asymptotic method and new iterative method. Scientific Reports, 11(3478 ), 1-20.
  • [7] Chen, S.B., Soradi-Zeid, S., Alipour, M., Chu, Y.M., G ́omez-Aguilar, J.F., & Jahanshahi, H. (2021). Optimal control of nonlinear time-delay fractional differential equations with Dickson polynomials. Fractals, 29(04), 2150079.
  • [8] Liao, S.J. (1992). The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems. Ph.D. Thesis, Shanghai Jiao Tong University.
  • [9] Liao, S.J. (2004). On the homotopy analysis method for nonlinear problems. Applied Mathematics and Computation, 147, 499-513.
  • [10] Liao, S.J. (2009). Notes on the homotopy analysis method: Some definitions and theorems. Communications in Nonlinear Science and Numerical Simulation, 14, 983-997.
  • [11] Spiegel, M.R. (1965). Theory and Problems of Laplace Transform. Schaum’s Outline Series, New York: McGraw-Hill.
  • [12] Watugala, G.K. (1993). Sumudu transform: a new integral transform to solve differentia lequations and control engineering problems. International Journal of Mathematical Education in Science and Technology, 24(1), 35-43.
  • [13] Khan, Z.H., & Khan, W.A. (2008). N-transform properties and applications. NUST Journal of Engineering Science, 1, 127-133.
  • [14] Elzaki, T.M., & Ezaki, S.M. (2011). On the ELzaki transform and ordinary differential equation with variable coefficients. Advances in Theoretical and Applied Mathematics, 6(1), 41-46.
  • [15] Aboodh, K.S. (2013). The new integrale transform Aboodh transform. Global Journal of Pure and Applied Mathematics, 9(1), 35-43.
  • [16] Maitama, S., & Zhao, W. (2019). New integral transform: Shehu transform a generalization of Sumudu and Laplace transform for solving differential equations. International Journal of Analysis and Applications, 17(2), 167-190.
  • [17] Khader, M.M., Kumar S., & Abbasbandy, S. (2013). New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology. Chinese Physics B, 22(11), 110201, 1-5.
  • [18] Gupta, V.G., & Kumar, P. (2015). Approximate solutions of fractional linear and nonlinear differential equations using Laplace homotopy analysis method. International Journal of Nonlinear Sciences, 19(2), 113-120.
  • [19] Saad, K.M., & AL-Shomrani, A.A. (2016). An application of homotopy analysis transform method for Riccati differential equation of fractional order. Journal of Fractional Calculus and Applications, 7(1), 61-72.
  • [20] Pandey, R.K., & Mishra, H.K. (2015). Numerical simulation of time-fractional fourth order differential equations via homotopy analysis fractional Sumudu transform method. American Journal of Numerical Analysis, 3(3), 52-64.
  • [21] Rathore, S., Kumarb, D., Singh, J., & Gupta, S. (2012). Homotopy analysis Sumudu transform method for nonlinear equations. International Journal of Industrial Mathematics, 4(4), 301-314.
  • [22] Khan, A., Junaid, M., Khan, I., Ali, F., Shah, K., & Khan, D. (2017). Application of homotopy natural transform method to the solution of nonlinear partial differential equations. Science International, 29(1), 297-303.
  • [23] Rida, S.Z., Arafa, A.A.A., Abedl-Rady, A.S., & Abdl-Rahim, H.R. (2017). Homotopy analysis natural transform for solving fractional physical models. International Journal of Pure and Applied Mathematics, 117(1), 19-32.
  • [24] Wang, K., & Liu, S. (2016). Application of new iterative transform method and modified fractional homotopy analysis transform method for fractional Fornberg-Whitham equation. Journal of Nonlinear Sciences and Applications, 9, 2419-2433.
  • [25] Ziane, D., & Hamdi Cherif, M. (2018). Homotopy analysis Aboodh transform method for nonlinear system of partial differential equations. Universal Journal of Mathematics and Applications, 1(4), 244-253.
  • [26] Maitama, S., & Zhao, W. (2020). New homotopy analysis transform method for solving multidimensional fractional diffusion equations. Arab Journal of Basic and Applied Sciences, 27(1), 27-44.
  • [27] Rangaig, N.A., Minor, N.D., Penonal, G.F.I., Filipinas, J.L.D.C., & Convicto, V.C. (2017). On another type of transform called Rangaig transform. International Journal of Partial Differential Equations and Applications, 5(1), 42-48.
  • [28] Mansour, E.A., & Kuffi, E.A. (2022). Generalization of Rangaig transform. International Journal of Nonlinear Analysis and Applications, 11(1), 2227-2231.
  • [29] Ziane, D., & Hamdi Cherif, M. (2015). Resolution of nonlinear partial differential equations by Elzaki transform decomposition method. Journal of Approximation Theory and Applied Mathematics, 5, 17-30.
  • [30] Ziane, D., Belgacem, R., & Bokhari, A. (2019). A new modified Adomian decomposition method for nonlinear partial differential equations. Open Journal of Mathematical Analysis, 3(2), 81-90.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a59d8f86-c4e4-405c-a429-d456f79e1470
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