Analytical Analysis of Fractional Order Swift-Hohenberg Equations

Aslam Zeb; Umar Farooq; Iqra Iqbal; Ghani Irfan

Analytical Analysis of Fractional Order Swift-Hohenberg Equations

Aslam Zeb, Umar Farooq, Iqra Iqbal, Ghani Irfan

Vol. 12, Issue 03, PP. 31-39, March 25

Keywords: New Approximate Analytical Method (NAAM), Swift-Hohenberg (S-H) Equations, Fractional Order Differential Equations, Analytical Solution, Numerical and Graphical Analysis

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This study utilizes the New Approximate Analytical Method (NAAM) to solve fractional order Swift-Hohenberg (S-H) equations, which model complex systems with memory and hereditary effects. By deriving approximate analytical solutions for both linear and nonlinear cases, NAAM simplifies the analytical analysis of these equations, particularly those involving fractional derivatives. A comparative evaluation with other traditional analytical and numerical methods highlights the NAAM’s effectiveness and accuracy, advancing the understanding of fractional systems and providing improved tools for addressing complex mathematical models.

Aslam Zeb, aslamzeb.uos@gmail.com, Department of Basic Sciences and Islamiat University of Engineering and Technology, Peshawar, Pakistan.
Umar Farooq, umarfarooq0216@gmail.com, Department of Mathematics, Abdul Wali Khan University Mardan, Pakistan.
Iqra Iqbal, iqra.iqbal5252@gmail.com, Department of Mathematics, Namal University Mianwali, Pakistan, Pakistan.
Ghani Irfan, ghani.irfan111@gmil.com, Department of Basic Sciences and Islamiat University of Engineering and Technology, Peshawar, Pakistan.

Aslam Zeb Umar Farooq Iqra Iqbal Ghani Irfan “Analytical Analysis of Fractional Order Swift-Hohenberg Equations” International Vol. 12 Issue 03 PP. 31-39 March 2025. https://doi.org/10.34259/ijew.25.12033139.

[1] Zheng, B., 2023. Ordinary Differential Equation and Its Application. Highlights in Science, Engineering and Technology, 72, pp.645-651.

[2] Restivo, S., 2001. Mathematics in society and history: Sociological inquiries (Vol. 20). Springer Science & Business Media.

[3] Fraser, C., 1985. JL Lagrange changing approach to the foundations of the calculus of variations. Archive for History of Exact Sciences, 32, pp.151-191.

[4] Rößler, A., 2010. Runge–Kutta methods for the strong approximation of solutions of stochastic differential equations. SIAM Journal on Numerical Analysis, 48(3), pp.922-952.

[5] De Castro, A.B., Gómez, D. and Salgado, P., 2014. Mathematical models and numerical simulation in electromagnetism (Vol. 74). Springer.

[6] BUBAKAR, S.S., IBRAHIM, M. and ABUBAKAR, N., 2019. A STUDY ON SOME APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS IN HEAT TRANSFER. Journal of Applied Physical Science International, 11(3), pp.88-94.

[7] Farooq, U., Khan, H., Tchier, F., Hincal, E., Baleanu, D., & Bin Jebreen, H. (2021). New approximate analytical technique for the solution of time fractional fluid flow models. Advances in Difference Equations, 2021(1), 1-20.

[8] Nonlaopon, K., Alsharif, A. M., Zidan, A. M., Khan, A., Hamed, Y. S., & Shah, R. (2021). Numerical investigation of fractional-order Swift–Hohenberg equations via a Novel transform. Symmetry, 13(7), 12-63.

[9] Shah, R., Farooq, U., Khan, H., Baleanu, D., Kumam, P. and Arif, M., 2020. Fractional view analysis of third order Kortewege-De Vries equations, using a new analytical technique. Frontiers in Physics, 7, p.244.

[10] Singh, B.K. and Kumar, P., 2018. FRDTM for numerical simulation of multi-dimensional, time-fractional model of Navier–Stokes equation. Ain Shams Engineering Journal, 9(4), pp.827-834