A new coupling method of khalouta transform and residua lpower series method for solving nonlinear fractional hyperbolic-like equations with variable coefficients

• Autorzy: Khalouta Ali

Identyfikatory

DOI

10.17512/jamcm.2025.1.03

• Języki publikacji: EN

Abstrakty

EN

In this paper, we develop a new numerical method called Khalouta residual power series method (KHRPSM) by mixing the Khalouta transform method and the residual power series method for solving nonlinear fractional hyperbolic-like equations with variable coefficients. The KHRPSM resolves nonlinear fractional problems without resorting to He’s polynomials and Adomian polynomials. Therefore, the small computational size of this method is the strength of the scheme, which is an advantage compared with various series solution methods. The approximate and exact solutions of a numerical example of the proposed problem are demonstrated by the presented method. The numerical and exact solutions are compared with each other. The obtained results show that KHRPSM is easy to implement and highly effective in constructing approximate analytical solutions to nonlinear fractional problems arising in related fields of science and technology.

Słowa kluczowe

EN

hyperbolic-like equations; Caputo fractional derivative; Khalouta transform method; residual power series method; truncated series solutions

PL

równania hiperboliczne; pochodna ułamkowa Caputo; metoda transformacji Khalouty; metoda szeregów potęgowych reszt; rozwiązania szeregów uciętych

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2025
• Tom: Vol. 24, nr 1
• Strony: 30--43
• Opis fizyczny: Bibliogr. 22 poz., rys., tab.

Twórcy

autor

Khalouta Ali

• Laboratory of Fundamental Mathematics and Numerical Department of Mathematics, Faculty of Sciences Setif 1 University-Ferhat ABBAS, Algeria

Bibliografia

• [1] Akinyemi, L., & Iyiola, O. (2020). Exact and approximate solutions of time-fractional models arising from physics via Shehu transform. Mathematical Method in Applied Sciences, 43(12), 7442-7464.
• [2] Alhasan, A.S.H., Saranya, S., & Al-Mdallal, Q.M. (2024). Fractional derivative modeling of heat transfer and fluid flow around a contracting permeable infinite cylinder: Computational study. Partial Differential Equations in Applied Mathematics, 11, 100794, DOI: 10.1016/j.padiff.2024 .100794.
• [3] Shen, L.J. (2020). Fractional derivative models for viscoelastic materials at finite deformations. International Journal of Solids and Structures, 190, 226-237.
• [4] Ganie, A.H., Mofarreh, F., Alharthi, N.S., & Khan, A. (2025). Novel computations of the time-fractional chemical Schnakenberg mathematical model via non-singular kernel operators. Boundary Value Problems, 2025(2), DOI: 10.1186/s13661-024-01979-4.
• [5] Al-Qurashi, M., Rashid, S., Sultana, S. Jarad, F., & Alsharif, A.M. (2022). Fractional-order partial differential equations describing propagation of shallow water waves depending on power and Mittag-Leffler memory. AIMS Mathematics, 7(7), 12587-12619. DOI: 10.3934/math .2022697.
• [6] Khalouta, A. (2024). Existence, uniqueness and convergence solution of nonlinear Caputo--Fabrizio fractional biological population model. Sahand Communications in Mathematical Analysis, 21(3), 165-196, DOI: 10.22130/scma.2023.2005194.1360.
• [7] Ibrahim, R.W., Jalab, H.A., Karim, F.K., Alabdulkreem, E., & Ayub, M.N. (2022). A medical image enhancement based on generalized class of fractional partial differential equations. Quantitative Imaging in Medicine and Surgery, 12(1), 172-183. DOI: 10.21037/qims-21-15.
• [8] Abro, K.A. (2022). Numerical study and chaotic oscillations for aerodynamic model of wind turbine via fractal and fractional differential operators. Numerical Methods for Partial Differential Equations, 38(5), 1180-1194.
• [9] Saber, S. (2024). Control of chaos in the Burke-Shaw system of fractal-fractional order in the sense of Caputo-Fabrizio. Journal of Applied Mathematics and Computational Mechanics, 23(1), 83-96, DOI: 10.17512/jamcm.2024.1.07.
• [10] Chauhan, R.P., Kumar, S., Alkahtani, B.S.T., & Alzaid, S.S. (2024). A study on fractional order f inancial model by using Caputo–Fabrizio derivative. Results in Physics, 57, 107335.
• [11] Qin, Y., Khan, A., Ali, I., Al Qurashi, M., Khan, H., Shah, R., & Baleanu, D. (2020). An efficient analytical approach for the solution of certain fractional-order dynamical systems. Energies, 13, 1-14.
• [12] Jannelli, A. (2020). Numerical solutions of fractional differential equations arising in engineering sciences. Mathematics, 8(2), 215, DOI: 10.3390/math8020215.
• [13] Shukur, A.M. (2015). Adomian decomposition method for certain space-time fractional partial differential equations. IOSR Journal of Mathematics, 11(1), 55-65.
• [14] Yin, X.B., Kumar, S., & Kumar, D. (2015). A modified homotopy analysis method for solution of fractional wave equations. Advances in Mechanical Engineering, 7(12), 1-8.
• [15] Hamdi-Cherif, M., Belghaba, K., &Ziane, D.(2016).Homotopyperturbationmethodforsolving the fractional Fisher’s equation. International Journal of Analysis and Applications, 10(1), 9-16.
• [16] Arikoglu, A., & Ozkol, I. (2007). Solution of fractional differential equations by using differential transform method. Chaos, Solitons & Fractals, 34(5), 1473-1481.
• [17] Singh, B.K., & Kumar, P. (2017). Fractional variational iteration method for solving fractional partial differential equations with proportional delay. International Journal of Differential Equations, 2017, DOI: 10.1155/2017/5206380.
• [18] Khalouta, A. (2023). A new exponential type kernel integral transform: Khalouta transform and its applications. Mathematica Montisnigri, 57, 5-23, DOI: 10.20948/mathmontis-2023-57-1.
• [19] El-Ajou, A., Abu Arqub, O., Al Zhour, Z., & Momani, Sh. (2013). New results on fractional power series: theories and applications. Entropy, 15(12), 5305-5323.
• [20] Kilbas, A.A., Srivastava, H.M., & Trujillo, J.J. (20036). Theory and Application of Fractional Differential equations. Elsevier, North-Holland.
• [21] Khalouta, A. (2024). Khalouta transform via different fractional derivative operators. Estn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki, 28(2), 407-425, DOI: 10.14498/vsgtu2082.
• [22] Khalouta, A. (2022). A novel iterative method to solve nonlinear wave-like equations of fractional order with variable coefficients. Revista Colombiana de Matematicas, 56(1), 13-34.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).