Browsing by Author "Alhazmi, Sharifah E."

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    A Novel Analysis of Generalized Perturbed Zakharov–Kuznetsov Equation of Fractional-Order Arising in Dusty Plasma by Natural Transform Decomposition Method
    (Hindawi, 2022-06) Alhazmi, Sharifah E.; Abdelmohsen, Shaimaa A. M.; Alyami, Maryam Ahmed; Ali, Aatif; Asamoah, Joshua Kiddy K.; 0000-0002-7066-246X
    The natural transform decomposition method (NTDM) is a relatively new transformation method for finding an approximate differential equation solution. In the current study, the NTDM has been used for obtaining an approximate solution of the fractional-order generalized perturbed Zakharov–Kuznetsov (GPZK) equation. The method has been tested for three nonlinear cases of the fractional-order GPZK equation. The absolute errors are analyzed by the proposed method and the q-homotopy analysis transform method (q-HATM). 3D and 2D graphs have shown the proposed method’s accuracy and effectiveness. NTDM gives a much-closed solution after a few terms.
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    Numerical Investigation of Fractional-Order Kawahara and Modified Kawahara Equations by a Semianalytical Method
    (Hindawi, 2022-02) Alhejaili, Weaam; Alhazmi, Sharifah E.; Nawaz, Rashid; Ali, Aatif; Asamoah, Joshua Kiddy K.; Zada, Laiq; 0000-0002-7066-246X
    In this work, the optimal homotopy asymptotic method (OHAM) has been used to find approximate solutions to the nonlinear fractional-order Kawahara and modified Kawahara equations. The method convergence is controlled by a flexible function known as the auxiliary function. The values of the unknown arbitrary constants in the auxiliary function are computed using the Caputo derivative fractional-order and the well-known approach of least squares. Fractional-order derivatives are taken in the Caputo sense with numerical values in the closed interval ½0, 1 . The suggested method is directly applied to fractional-order Kawahara and modified Kawahara equations, with no need for small or large parameter assumptions. The numerical results obtained by the proposed method are compared to the new iterative method (NIM). Results reveal that the proposed method converges faster to the exact solution than other methods in the literature
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    Numerical Investigation of Fractional-Order Kawahara and Modified Kawahara Equations by a Semianalytical Method
    (Hindawi, 2022-02) Alhejaili, Weaam; Alhazmi, Sharifah E.; Nawaz, Rashid; Ali, Aatif; Asamoah, Joshua Kiddy K.; Zada, Laiq; 0000-0002-7066-246X
    In this work, the optimal homotopy asymptotic method (OHAM) has been used to find approximate solutions to the nonlinear fractional-order Kawahara and modified Kawahara equations. The method convergence is controlled by a flexible function known as the auxiliary function. The values of the unknown arbitrary constants in the auxiliary function are computed using the Caputo derivative fractional-order and the well-known approach of least squares. Fractional-order derivatives are taken in the Caputo sense with numerical values in the closed interval ½0, 1 . The suggested method is directly applied to fractional-order Kawahara and modified Kawahara equations, with no need for small or large parameter assumptions. The numerical results obtained by the proposed method are compared to the new iterative method (NIM). Results reveal that the proposed method converges faster to the exact solution than other methods in the literature.
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    Numerical Investigation of Fractional-Order Kawahara and Modified Kawahara Equations by a Semianalytical Method
    (Hindawi, 2022-02) Alhejaili, Weaam; Alhazmi, Sharifah E.; Nawaz, Rashid; Ali, Aatif; Asamoah, Joshua Kiddy K.; Zada, Laiq; 0000-0002-7066-246X
    In this work, the optimal homotopy asymptotic method (OHAM) has been used to find approximate solutions to the nonlinear fractional-order Kawahara and modified Kawahara equations. The method convergence is controlled by a flexible function known as the auxiliary function. The values of the unknown arbitrary constants in the auxiliary function are computed using the Caputo derivative fractional-order and the well-known approach of least squares. Fractional-order derivatives are taken in the Caputo sense with numerical values in the closed interval ½0, 1 . The suggested method is directly applied to fractional-order Kawahara and modified Kawahara equations, with no need for small or large parameter assumptions. The numerical results obtained by the proposed method are compared to the new iterative method (NIM). Results reveal that the proposed method converges faster to the exact solution than other methods in the literature.