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    Analysis of some dynamical systems by combination of two different methods
    (Nature Portfolio, 2024) Ganie, Abdul Hamid; Zidan, A. M.; Shah, Rasool; Akguel, Ali; Hassani, Murad Khan
    In this study, we introduce a novel iterative method combined with the Elzaki transformation to address a system of partial differential equations involving the Caputo derivative. The Elzaki transformation, known for its effectiveness in solving differential equations, is incorporated into the proposed iterative approach to enhance its efficiency. The system of partial differential equations under consideration is characterized by the presence of Caputo derivatives, which capture fractional order dynamics. The developed method aims to provide accurate and efficient solutions to this complex mathematical system, contributing to the broader understanding of fractional calculus applications in the context of partial differential equations. Through numerical experiments and comparisons, we demonstrate the efficacy of the proposed Elzaki-transform-based iterative method in handling the intricate dynamics inherent in the given system. The study not only showcases the versatility of the Elzaki transformation but also highlights the potential of the developed iterative technique for addressing similar problems in various scientific and engineering domains.
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    Comparative study of fractional Newell-Whitehead-Segel equation using optimal auxiliary function method and a novel iterative approach
    (Aip Publishing, 2024) Xin, Xiao; Khan, Ibrar; Ganie, Abdul Hamid; Akgul, Ali; Bonyah, Ebenezer; Fathima, Dowlath; Yousif, Badria Almaz Ali
    This research explores the solution of the time-fractional Newell-Whitehead-Segel equation using two separate methods: the optimal auxiliary function method and a new iterative method. The Newell-Whitehead-Segel equation holds significance in modeling nonlinear systems, particularly in delineating stripe patterns within two-dimensional systems. Employing the Caputo fractional derivative operator, we address two case study problems pertaining to this equation through our proposed methods. Comparative analysis between the numerical results obtained from our techniques and an exact solution reveals a strong alignment. Graphs and tables illustrate this alignment, showcasing the effectiveness of our methods. Notably, as the fractional orders vary, the results achieved at different fractional orders are compared, highlighting their convergence toward the exact solution as the fractional order approaches an integer. Demonstrating both interest and simplicity, our proposed methods exhibit high accuracy in resolving diverse nonlinear fractional order partial differential equations. (c) 2024 Author(s).
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    Correction to: Analysis of some dynamical systems by combination of two different methods (Scientific Reports, (2024), 14, 1, (18710), 10.1038/s41598-024-62042-x)
    (Nature Research, 2024) Ganie, Abdul Hamid; Zidan, A.M.; Shah, Rasool; Akgül, Ali; Hassani, Murad Khan
    Correction to: Scientific Reportshttps://doi.org/10.1038/s41598-024-62042-x, published online 12 August 2024 In the original version of this Article A. M. Zidan was incorrectly affiliated with ‘Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon’. The correct affiliation is listed below. Department of Mathematics, College of Science, King Khalid University, P.O. Box: 9004, 61413 Abha, Saudi Arabia. In addition, the Acknowledgements section contained an error. “The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through large group Research Project under Grant No. RGP.2/13/44.” now reads: “The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through large group Research Project under grant number RGP.2/16/45.” The original Article has been corrected. © The Author(s) 2024.