Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 21Citation - Scopus: 24Dynamics 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; Afouna, Nour Abu; MatematikIn 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.Article Citation - WoS: 14Citation - Scopus: 28The Duffing Model Endowed With Fractional Time Derivative and Multiple Pantograph Time Delays(Editura Acad Romane, 2019) Alqurana, Marwan; Baleanu, Dumitru; Jaradat, Imad; Baleanu, Dumitru; Syam, Muhammed; Muhammed, Syam; Alquran, Marwan; MatematikIn this work, we are concerned with presenting a novel study on the generalized reaction Duffing model involving two actions on the time coordinate: fractional time derivative and multiple pantograph time delays. The modified fractional Maclaurin series is suggested to suit and treat the presence of these time actions. Graphical analysis in support of the impact of fractional order and delay parameters on the dynamics of the Duffing model is performed. One of the findings that has been drawn in this research is to give a reasonable description of one of the cases of physical meaning of fractional derivative.Article Citation - WoS: 24Citation - Scopus: 26Chaotic and Solitonic Solutions for a New Time-Fractional Two-Mode Korteweg-De Vries Equation(Editura Acad Romane, 2020) Alquran, Marwan; Baleanu, Dumitru; Jaradat, Imad; Momani, Shaher; Baleanu, Dumitru; MatematikThe two-mode Korteweg-de Vries (TMKdV) equation is a nonlinear dispersive wave model that describes the motion of two different directional wave modes with the same dispersion relations but with various phase velocities, nonlinearity, and dispersion parameters. In this work, we study the dynamics of the model analytically in a time-fractional sense to ensure the stability of the extracted waves of the TMKdV equation. We use the fractional power series technique to conduct our analysis. We show that there is a homotopy mapping of the solution as the Caputo time-fractional derivative order varies over (0,1] and that both waves have the same physical shapes but with reflexive relation.Article Citation - WoS: 14Citation - Scopus: 17On (2+1)-Dimensional Physical Models Endowed With Decoupled Spatial and Temporal Memory Indices<sup>☆</Sup>(Springer Heidelberg, 2019) Alquran, Marwan; Yousef, Feras; Momani, Shaher; Baleanu, Dumitru; Jaradat, Imad.The current work concerns the development of an analytical scheme to handle (2 + 1) -dimensional partial differential equations endowed with decoupled spatial and temporal fractional derivatives (abbreviated by (alpha,beta) -models). For this purpose, a new bivariate fractional power series expansion has been integrated with the differential transform scheme. The mechanism of the submitted scheme depends mainly on converting the (alpha,beta) -model to a recurrence-differential equation that can be easily solved by virtue of an iterative procedure. This, in turn, reduces the computational cost of the Taylor power series method and consequently introduces a significant refinement for solving such hybrid models. To elucidate the novelty and efficiency of the proposed scheme, several (alpha,beta) -models are solved and the presence of remnant memory, due to the fractional derivatives, is graphically illustrated.Article AN ANALYTICAL STUDY OF (2+1)-DIMENSIONAL PHYSICAL MODELS EMBEDDED ENTIRELY IN FRACTAL SPACE(Editura ACAD Romane, 2019) Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; Abdel-Muhsen, RuwaIn this article, we analytically furnish the solution of (2 + 1)-dimensional fractional differential equations, with distinct fractal-memory indices in all coordinates, as a trivariate (alpha, beta, gamma)-fractional power series representation. The method is tested on several physical models with inherited memories. Moreover, a version of Taylor's theorem in fractal three-dimensional space is presented. As a special case, the solutions of the corresponding integer-order cases are extracted by letting alpha, beta, gamma -> 1, which indicates to some extent for a sequential memory.Article Citation - WoS: 15Citation - Scopus: 18New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices(Asme, 2019) Alquran, Marwan; Jaradat, Imad; Momani, Shaher; Baleanu, Dumitru; Yousef, FerasHerein, analytical solutions of three-dimensional (3D) diffusion, telegraph, and Burgers' models that are equipped with three memory indices are derived by using an innovative fractional generalization of the traditional differential transform method (DTM), namely, the threefold-fractional differential transform method (threefold-FDTM). This extends the applicability of DTM to comprise initial value problems in higher fractal spaces. The obtained solutions are expressed in the form of a (gamma) over bar -fractional power series which is a fractional adaptation of the classical Taylor series in several variables. Furthermore, the projection of these solutions into the integer space corresponds with the solutions of the classical copies for these models. The results detect that the suggested method is easy to implement, accurate, and very efficient in (non)linear fractional models. Thus, research on this trend is worth tracking.Article Citation - WoS: 13Citation - Scopus: 17The 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, MarwanIn 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.Article Citation - WoS: 12Citation - Scopus: 16An Avant-Garde Handling of Temporal-Spatial Fractional Physical Models(Walter de Gruyter Gmbh, 2020) Alquran, Marwan; Katatbeh, Qutaibeh; Yousef, Feras; Momani, Shaher; Baleanu, Dumitru; Jaradat, ImadIn the present study, we dilate the differential transform scheme to develop a reliable scheme for studying analytically the mutual impact of temporal and spatial fractional derivatives in Caputo's sense. We also provide a mathematical framework for the transformed equations of some fundamental functional forms in fractal 2-dimensional space. To demonstrate the effectiveness of our proposed scheme, we first provide an elegant scheme to estimate the (mixed-higher) Caputo-fractional derivatives, and then we give an analytical treatment for several (non)linear physical case studies in fractal 2-dimensional space. The study concluded that the proposed scheme is very efficacious and convenient in extracting solutions for wide physical applications endowed with two different memory parameters as well as in approximating fractional derivatives.