Yazar "Nawaz, Rashid" seçeneğine göre listele

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    Öğe
    Comparative analysis of the fractional order Cahn-Allen equation
    (Elsevier B.V., 2023) Khan, Ibrar; Nawaz, Rashid; Ali, Ali Hasan; Akgul, Ali; Lone, Showkat Ahmad
    This current work presents a comparative study of the fractional-order Cahn-Allen (CA) equation, where the non-integer derivative is taken in the Caputo sense.The Cahn-Allen equation is an equation that assists in the comprehension of phase transitions and pattern formation in physical systems. This equation describes how different phases of matter, such as solids and liquids, change and interact throughout time. We employ two analytical methods: the Laplace Residual Power Series Method (LRPSM) and the New Iterative Method (NIM), to solve the proposed model. The LRPSM is a combination of the Laplace Transform and the Residual Power Series Method, while the New Iterative Method is a modified form of the Adomian Decomposition Method that does not require any type of polynomial or digitization. For the purpose of accuracy and reliability, we compare our findings with other methods and the exact solution used in the literature. Additionally, 2D and 3D plots are generated for various fractional order values denoted as p. These plots illustrate that as the fractional order p approaches 1, the graph of the approximate solution gradually coincides with the graph of the exact solution. © 2023 The Author(s)
  • [ X ]
    Öğe
    Numerical investigation of generalized perturbed Zakharov-Kuznetsov equation of fractional order in dusty plasma
    (Taylor & Francis Ltd, 2022) Ali, Nasir; Nawaz, Rashid; Zada, Laiq; Nisar, Kottakkaran Sooppy; Ali, Zahid; Jamshed, Wasim; Hussain, Syed M.
    In the present work, the new iterative method with a combination of the Laplace transform of the Caputo's fractional derivative has been applied to the generalized (3 + 1) dimensional fractional perturbed Zakharov-Kuznetsov equation in a dusty plasma. The proposed method is applied without any discretization and linearization. The numerical and graphical results show the accuracy of the proposed method for nonlinear differential equations. Moreover, the methods are easy to implement and give the efficient approximate solutions.