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Browsing by Author "Ali, Mohammed"

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    Article
    Citation - WoS: 21
    Citation - Scopus: 24
    Dynamics of Integer-Fractional Time-Derivative for the New Two-Mode Kuramoto-Sivashinsky Model
    (Editura Acad Romane, 2020) Ali, Mohammed; Baleanu, Dumitru; Alquran, Marwan; Jaradat, Imad; Abu Afouna, Nour; Baleanu, Dumitru; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    In this paper, we investigate the dynamics of a nonlinear model responsible for the transition of turbulence phenomena and cellular instabilities to a chaos. The two-mode Kuramoto-Sivashinsky (TMKS) model is an example of such application. We study both integer and fractional time-derivative involved in this model. Solitary wave solutions and approximate analytical solutions will be derived to TMKS model by means of well-posed different techniques. The mechanism of the concepts of two-mode and time-fractional derivative will be discussed in this work. Finally, both 2-dimensional and 3-dimensional plots will be provided to support our findings.
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    Article
    Citation - WoS: 13
    Citation - Scopus: 17
    The Dynamics of New Dual-Mode Kawahara Equation: Interaction of Dual-Waves Solutions and Graphical Analysis
    (Iop Publishing Ltd, 2020) Jaradat, Imad; Ali, Mohammed; Baleanu, Dumitru; Alquran, Marwan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    In this paper, we introduce a new dual-mode Kawahara equation with new dissipative, nonlinearity and interaction phase velocity parameters. Also, we study the solutions of this model by using the tanh-scheme, Kudryashov-scheme and the sine-cosine function methods. Dynamics and shapes of the obtained solutions are illustrated by using graphical 2D and 3D plots. Finally, the interaction of the obtained dual-waves has been linked with the change of the phase-velocity parameter.
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    Article
    Citation - WoS: 20
    Citation - Scopus: 22
    Stationary Wave Solutions for New Developed Two-waves' Fifth-Order Korteweg-De Vries Equation
    (Springeropen, 2019) Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; Ali, Mohammed; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    In this work, we present a new two-waves' version of the fifth-order Korteweg-de Vries model. This model describes the propagation of moving two-waves under the influence of dispersion, nonlinearity, and phase velocity factors. We seek possible stationary wave solutions to this new model by means of Kudryashov-expansion method and sine-cosine function method. Also, we provide a graphical analysis to show the effect of phase velocity on the motion of the obtained solutions.