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: 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: 15Citation - Scopus: 19Optical Wave Propagation To a Nonlinear Phenomenon With Pulses in Optical Fiber(Springer, 2023) Sulaiman, Tukur Abdulkadir; Alshomrani, Ali S.; Yusuf, Abdullahi; Alquran, Marwan; Baleanu, Dumitru; Jaradat, ImadWe examine the three-component coupled nonlinear Schrodinger equation that is used for the propagation of pulses to the nonlinear optical fiber. Multi-component NLSE equations have gained popularity because they can be used to demonstrate a vast array of complex observable systems as well as more kinetic patterns of localized wave solutions. The solutions are obtained by using the generalized exponential rational function method, a relatively new integration tool. We extract various optical solitons in different forms. Moreover, exponential, periodic solutions and solutions of the hyperbolic type are guaranteed. In addition to providing previously extracted solutions, the used approach also extracts new exact solutions and is beneficial for elucidating nonlinear partial differential equations. The graphs of different shapes are sketched for the attained solutions and some physical properties- are raised. The reported solutions in this work are new as they are compared to earlier similar studies. The results of this paper show that the used method is effective at improving the nonlinear dynamical behavior of a system. The findings show that the computational approach taken is successful, simple, and applicable even to complicated phenomena.Article Citation - WoS: 7Citation - Scopus: 8Numerical Simulation of the Fractional Diffusion Equation(World Scientific Publ Co Pte Ltd, 2023) Yusuf, Abdullahi; Jarad, Fahd; Sulaiman, Tukur A.; Alquran, Marwan; Partohaghighi, MohammadDuring this paper, a specific type of fractal-fractional diffusion equation is presented by employing the fractal-fractional operator. We present a reliable and accurate operational matrix approach using shifted Chebyshev cardinal functions to solve the considered problem. Also, an operational matrix for the considered derivative is obtained from basic functions. To solve the introduced problem, we convert the main equation into an algebraic system by extracting the operational matrix methods. Graphs of exact and approximate solutions along with error graphs are presented. These figures show how the introduced approach is reliable and accurate. Also, tables are established to illustrate the values of solutions and errors. Finally, a comparison of the solutions at a specific time is given for each test problem.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: 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.