Yasser-Jassim Transform–Variational Framework for Solving Selected Fractional Partial Differential Equations

المؤلفون

  • Sameehah.alkaleeli Alkaleeli Faculty of Arts and Sciences / Benghazi University

DOI:

https://doi.org/10.36602/jsba.2026.22.11

الملخص

The primary disinterested of this examination is to develop an innovative analytical technique for solving both linear and nonlinear fractional partial differential equations (FPDEs) by integrating the Variational Iteration Method (VIM) with the Yasser-Jassim Transform. This mixture approach utilises the strengths of both methods to convert fractional derivatives into algebraic forms, simplifying the solution procedure. The Yasser-Jassim Transform excels at handling fractional derivatives, while the Variational Iteration Method provides a solid foundation for developing iterative solutions.

Some well-known equations serve to illustrate the validity and effectiveness of our integrated technique for treating FPDEs.

المراجع

[1] M. M. El-Borai, W. G. El-Sayed, and A. M. Jawad, “Adomian Decomposition Method For Solving Fractional Differential Equations,”

vol. 02, no. 06.

[2] S. Momani and A. Yıldırım, “Analytical approximate solutions of the fractional convection–diffusion equation with nonlinear

source term by He’s homotopy perturbation method,” Int. J. Comput. Math., vol. 87, no. 5, pp. 1057–1065, Apr. 2010, doi:10.1080/00207160903023581.

[3] A. A. H. Mtawal and S. R. Alkalee, “A new modified homotopy perturbation method for fractional partial differential equations with proportional delay,” J. Adv. Math., vol. 19, pp. 58–73, Oct. 2020, doi: 10.24297/jam.v19i.8876.

[4] M. Tatari and M. Dehghan, “On the convergence of He’s variational iteration method,” J. Comput. Appl. Math., vol. 207, no. 1, pp. 121–128, 2007.

[5] J. H. He, “A variational iteration approach to nonlinear problems and its applications,” Mech Appl, vol. 20, no. 1, pp. 30–31, 1998.

[6] J. Iqbal, K. Shabbir, and L. Guran, “Semianalytical Solutions of Some Nonlinear Time Fractional Models Using Variational Iteration Laplace Transform Method,” J. Funct. Spaces, vol. 2021, pp. 1–9, Nov. 2021, doi: 10.1155/2021/8345682.

[7] A. S. Abedl-Rady, S. Z. Rida, A. A. M. Arafa, and H. R. Abedl-Rahim, “Variational iteration sumudu transform method for solving fractional nonlinear gas dynamics equation,” Int J Res Stu Sci Eng Tech, vol. 1, pp. 82–90, 2014.

[8] M. H. Cherif and D. Ziane, “Variational iteration method combined with new transform to solve fractional partial

differential equations,” Univers. J. Math. Appl., vol. 1, no. 2, pp. 113–120, 2018.

[9] A. Boulekhras and K. Belghaba, “Shehu Variational Iteration Method For Solve Some Fractional Differential Equations,” Commun. Math. Appl., vol. 13, no. 3, pp. 1207–1219, Nov. 2022, doi: 10.26713/cma.v13i3.1906.

[10] M. T. Yasser and H. K. Jassim, “A new integral transform for solving integral and ordinary differential equations,” Math.

Comput. Sci., vol. 6, no. 2, pp. 32–42, 2025.

[11] R. Belgacem, D. Baleanu, and A. Bokhari, “Shehu transform and applications to Caputo-fractional differential equations,”

Int. J. Anal. Appl., vol. 17, no. 6, pp. 917-927, 2019.

[12] S. Kumar, “A new fractional modeling arising in engineering sciences and its analytical approximate solution,” Alex. Eng. J., vol. 52, no. 4, pp. 813–819, 2013.

[13] D. Zı̇ Ane, T. M. Elzakı̇ , and M. Hamdı̇ Cherı̇ F, “Elzaki transform combined with variational iteration method for partial

differential equations of fractional order,” Fundam. J. Math. Appl., vol. 1, no. 1, pp. 102–108, Jun. 2018, doi: 10.33401/fujma.415892.

[14] S. A. Sachit and H. K. Jassim, “A Modified Iterative Approach Using YJ Transform for Solving Fractional PDEs,” Prog. Fract. Differ. Appl., vol. 11, no. 4, pp. 661–676, Oct. 2025 doi:10.18576/pfda/110403.

[15] A. Khalouta, “Exact solution of nonlinear time-fractional reaction-diffusionconvection equation via a new coupling

method,” Int. J. Nonlinear Anal. Appl., vol. 13, no. 2, pp. 333–344, 2022.

[16] J. He, “A new approach to nonlinear partial differential equations,” Commun. Nonlinear Sci. Numer. Simul., vol. 2, no. 4,

pp. 230–235, 1997.

[17] J. Singh, D. Kumar, and A. Kılıçman, “Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using

Sumudu Transform,” Abstr. Appl. Anal., vol. 2013, pp. 1–8, 2013, doi: 10.1155/2013/934060.

[18] R. Al-deiakeh, S. Alhazmi, S. Al- Omari, M. Al-Smadi, and S. Momani, “On the Laplace Residual Series Method and Its

Application to Time-Fractional Fisher’s Equations,” Fractal Fract., vol. 9, no. 5, p. 275, May 2025, doi: 10.3390/fractalfract9050275.

منشور

2026-09-11

كيفية الاقتباس

Alkaleeli, S. (2026). Yasser-Jassim Transform–Variational Framework for Solving Selected Fractional Partial Differential Equations . مجلة العلوم الاساسية و التطبيقية, (22), 11–19. https://doi.org/10.36602/jsba.2026.22.11

إصدار

القسم

Articles