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    A Comparative Analysis of the Fractional-Order Coupled Korteweg-De Vries Equations with the Mittag-Leffler Law
    (Hindawi Ltd, 2022) Aljahdaly, Noufe H.; Akgul, Ali; Shah, Rasool; Mahariq, Ibrahim; Kafle, Jeevan
    This article applies efficient methods, namely, modified decomposition method and new iterative transformation method, to analyze a nonlinear system of Korteweg-de Vries equations with the Atangana-Baleanu fractional derivative. The nonlinear fractional coupled systems investigated in this current analysis are the system of Korteweg-de Vries and the modified system of Korteweg-de Vries equations applied as a model in nonlinear physical phenomena arising in chemistry, biology, physics, and applied sciences. Approximate analytical results are represented in the form of a series with straightforward components, and some aspects showed an appropriate dependence on the values of the fractional-order derivatives. The convergence and uniqueness analysis is carried out. To comprehend the analytical procedure of both methods, three test examples are provided for the analytical results of the time-fractional KdV equation. Additionally, the efficiency of the mentioned procedures and the reduction in calculations provide broader applicability. It is also illustrated that the findings of the current methodology are in close harmony with the exact solutions. The series result achieved applying this technique is proved to be accurate and reliable with minimal calculations. The numerical simulations for obtained solutions are discussed for different values of the fractional order.
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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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    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.
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    Exact analysis of electro-osmotic flow of Walters'-B fluid with non-singular kernel
    (Indian Acad Sciences, 2021) Sunthrayuth, Pongsakorn; Alderremy, Aisha; Aly, Shaban; Shah, Rasool; Akgul, Ali
    Applying the electric field to a fluid flowing on an infinite vertical plate is the most recent technique used for studying fluid movement. This technique is known as electro-osmotic flow (EOF). Therefore, the core aim of the present research work is to examine the time-dependent electro-osmotic flow of viscoelastic fluid on a vertical flat plate together with the effects of heat generation and chemical reaction. The classical system of governing equations has been fractionalised by means of Caputo-Fabrizio's time-fractional derivative. Governing equations have been non-dimensionalised by using relative dimensionless quantities. The exact solutions for the momentum, temperature and concentration equations have been developed by implementing the Laplace transform technique. For graphical analysis, the solutions have been plotted against the inserted parameters using the computational software Mathematica. It is interesting to mention that the time-fractional model provides more than one fluid layer for the analysis of the fluid motion, heat distribution and mass concentration, which is not possible by assuming the classical mathematical model. It is also very important to mention that the velocity profile shows declination for greater values of electro-osmotic parameter Es.
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    On Solutions of Fractional-Order Gas Dynamics Equation by Effective Techniques
    (Hindawi Ltd, 2022) Iqbal, Naveed; Akgul, Ali; Shah, Rasool; Bariq, Abdul; Al-Sawalha, M. Mossa; Ali, Akbar
    In this work, the novel iterative transformation technique and homotopy perturbation transformation technique are used to calculate the fractional-order gas dynamics equation. In this technique, the novel iteration method and homotopy perturbation method are combined with the Elzaki transformation. The current methods are implemented with four examples to show the efficacy and validation of the techniques. The approximate solutions obtained by the given techniques show that the methods are accurate and easy to apply to other linear and nonlinear problems.