Homotopy perturbation Shehu transform method for solving fractional models arising in applied sciences

• Autorzy: Maitama Shehu , Zhao Weidong

Identyfikatory

DOI

10.17512/jamcm.2021.1.07

• Języki publikacji: EN

Abstrakty

EN

Using the recently proposed homotopy perturbation Shehu transform method (HPSTM), we successfully construct reliable solutions of some important fractional models arising in applied physical sciences. The nonlinear terms are decomposed using He’s polynomials, and the fractional derivative is calculated in the Caputo sense. Using the analytical method, we obtained the exact solution of the fractional diffusion equation, fractional wave equation and the nonlinear fractional gas dynamic equation.

Słowa kluczowe

EN

homotopy perturbation technique; Shehu transform; numeric computations; symbolic computations; fractional model

PL

metoda transformacji Shehu; model ułamkowy; obliczenia numeryczne; obliczenia symboliczne; technika homotopii; metoda perturbacji homotopii

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2021
• Tom: Vol. 20, nr 1
• Strony: 71--82
• Opis fizyczny: Bibliogr., 25 poz., rys.

Twórcy

autor

Maitama Shehu

• School of Mathematics, Shandong University, Jinan Shandong, China

autor

Zhao Weidong

• School of Mathematics, Shandong University, Jinan Shandong, China

Bibliografia

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• [2] Khalouta, A., & Kadem, A. (2020). A new iterative natural transform method for solving nonlinear Caputo time-fractional partial differential equations. Jordan Journal of Mathematics and Statistics, 13(3), 459-476.
• [3] Khalouta, A., & Kadem, A. (2020). Numerical comparison of FNVIM and FNHPM for solving a certain type of nonlinear Caputo time fractional partial differential equations. Annales Mathematicae Silesianae, 34(2), 203-221.
• [4] Khalouta, A., & Kadem, A. (2020). Solutions of nonlinear time-fractional wave-like equations with variable coefficients in the form of Mittag-Leffler functions. Thai Journal of Mathematics, 18(1), 411-424.
• [5] Maitama, S., & Zhao, W. (2020). Beyond Sumudu transform and natural transform: J-transform properties and applications. Journal of Applied Analysis and Computation, 10, 1223-1241.
• [6] Sharma, D., Samra, G.S., & Singh, P. (2020). Approximate solution for fractional attractor onedimensional Keller-Segel equations using homotopy perturbation sumudu transform method. Nonlinear Engineering, 9(1), 370-381.
• [7] 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.
• [8] Eltayeb, H., & Bachar, I. (2020). A note on singular two-dimensional fractional coupled Burger’s equation and triple Laplace Adomian decomposition method. Boundary Value Problems, 2020(2020), 1-17.
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• [10] Maitama, S., & Zhao, W. (2021). New Laplace-type integral transform for solving steady heattransfer problem. Thermal Science, 25, 1-12.
• [11] 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 Application, 17, 167-190.
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• [13] Atangana, A., & Baleanu, D. (2016). New fractional derivatives with non-local and non-singular kernel: Theory and application to heat transfer model. Thermal Science, 20(2), 763-769.
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• [15] Bekela, A.S., Belachew, M.T., & Wole, G.A. (2020). A numerical method using Laplace-like transform and variational theory for solving time-fractional nonlinear partial differential equations with proportional delay. Advances in Difference Equations, 2020:586.
• [16] Bokharia, A., Baleanu, D., & Belgacema, R. (2020). Application of Shehu transform to Atangana-Baleanu derivatives. Journal of Mathematics and Computer Science, 20, 101-107.
• [17] Aggarwal, S., Sharma, S.D., & Gupta, A.R. (2019). Application of Shehu transform for handling growth and decay problems. Global Journal of Engineering Science and Research, 6, 190-198.
• [18] Qureshi S., & Kumar P. (2019). Using Shehu transform to solve fractional order Caputo type initial value problems. Journal of Applied Mathematics and Computational Mechanics, 28, 75-83.
• [19] Ziane, D., & Cherif, M.H. (2020). Combination of two powerful methods for solving nonlinear differential equations. Earthline Journal of Mathematical Sciences, 3, 121-138.
• [20] Khan, H., Farooq, U., Rasool, S., Balaenu, D., & Kumam, Poom. (2020). Analytical solution of (2+time fractional order) physical models, using modified decomposition method. Applied Sciences, 10, 122.
• [21] Khalouta A., & Kadem, A. (2020). A comparative study of Shehu variational iteration method and Shehu decomposition method for solving nonlinear Caputo time-fractional wave-like equations with variable coefficients. Application and Applied Mathematics, 15(1), 430-445.
• [22] Akinyemi, L, & Iyiola, O. (2020). Exact and approximate solutions of time-fractional models arising from physics via Shehu transform. Mathematical Method in Applied Sciences, DOI: 10.1002/mma.6484, 1-23.
• [23] Khalouta, A., & Kadem, A. (2019). A new method to solve fractional differential equations: Inverse fractional Shehu transform method. Applications and Applied Mathematics, 14, 926-941.
• [24] Khalouta, A., & Kadem, A. (2020). A new modification of the reduced differential transform method for nonlinear fractional partial differential equations. Journal of Applied Mathematics and Computational Mechanics, 19(3), 45-58.
• [25] 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.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).