Yazar "Habib, Mustafa" seçeneğine göre listele

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    Öğe
    Approximate Solution of Nonlinear Time-Fractional Klein-Gordon Equations Using Yang Transform
    (Mdpi, 2022) Liu, Jinxing; Nadeem, Muhammad; Habib, Mustafa; Akgul, Ali
    The algebras of the symmetry operators for the Klein-Gordon equation are important for a charged test particle, moving in an external electromagnetic field in a space time manifold on the isotropic hydrosulphate. In this paper, we develop an analytical and numerical approach for providing the solution to a class of linear and nonlinear fractional Klein-Gordon equations arising in classical relativistic and quantum mechanics. We study the Yang homotopy perturbation transform method (YHPTM),which is associated with the Yang transform (YT) and the homotopy perturbation method (HPM), where the fractional derivative is taken in a Caputo-Fabrizio (CF) sense. This technique provides the solution very accurately and efficiently in the form of a series with easily computable coefficients. The behavior of the approximate series solution for different fractional-order p values has been shown graphically. Our numerical investigations indicate that YHPTM is a simple and powerful mathematical tool to deal with the complexity of such problems.
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    Öğe
    Numerical Investigation of Nonlinear Shock Wave Equations with Fractional Order in Propagating Disturbance
    (Mdpi, 2022) Fang, Jiahua; Nadeem, Muhammad; Habib, Mustafa; Akgul, Ali
    The symmetry design of the system contains integer partial differential equations and fractional-order partial differential equations with fractional derivative. In this paper, we develop a scheme to examine fractional-order shock wave equations and wave equations occurring in the motion of gases in the Caputo sense. This scheme is formulated using the Mohand transform (MT) and the homotopy perturbation method (HPM), altogether called Mohand homotopy perturbation transform (MHPT). Our main finding in this paper is the handling of the recurrence relation that produces the series solutions after only a few iterations. This approach presents the approximate and precise solutions in the form of convergent results with certain countable elements, without any discretization or slight perturbation theory. The numerical findings and solution graphs attained using the MHPT confirm that this approach is significant and reliable.