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: 13Citation - Scopus: 17Nonautonomous lump-periodic and analytical solutions tothe (3+1)-dimensional generalized Kadomtsev-Petviashviliequation(Springer, 2023) Alquran, Marwan; Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, DumitruThis work establishes the lump periodic and exact traveling wave solutions for the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation. We use the Hirota bilinear method, as well as the robust integration techniques tanh-coth expansion and rational sine-cosine, to provide such innovative solutions. In order to explain specific physical difficulties, innovative lump periodic and analytical solutions have been investigated. These discoveries have been proven to be useful in the transmission of long-wave and high-power communications networks. It is important to highlight that the results given in thiswork depict new features and reflect previously unknown physical dynamics for the governing model.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 Citation - WoS: 4Citation - Scopus: 5A New Analytical Method To Simulate the Mutual Impact of Space-Time Memory Indices Embedded in (1(de Gruyter Poland Sp Z O O, 2022) Jaradat, Imad; Alquran, Marwan; Baleanu, Dumitru; Makhadmih, MohammadIn the present article, we geometrically and analytically examine the mutual impact of space-time Caputo derivatives embedded in (1 + 2)-physical models. This has been accomplished by integrating the residual power series method (RPSM) with a new trivariate fractional power series representation that encompasses spatial and temporal Caputo derivative parameters. Theoretically, some results regarding the convergence and the error for the proposed adaptation have been established by virtue of the Riemann-Liouville fractional integral. Practically, the embedding of Schrodinger, telegraph, and Burgers' equations into higher fractional space has been considered, and their solutions furnished by means of a rapidly convergent series that has ultimately a closed-form fractional function. The graphical analysis of the obtained solutions has shown that the solutions possess a homotopy mapping characteristic, in a topological sense, to reach the integer case solution where the Caputo derivative parameters behave similarly to the homotopy parameters. Altogether, the proposed technique exhibits a high accuracy and high rate of convergence.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: 13Citation - Scopus: 17Nonautonomous Lump-Periodic and Analytical Solutions Tothe (3+1)-Dimensional Generalized Kadomtsev-Petviashviliequation(Springer, 2023) Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, Dumitru; Alquran, MarwanThis work establishes the lump periodic and exact traveling wave solutions for the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation. We use the Hirota bilinear method, as well as the robust integration techniques tanh-coth expansion and rational sine-cosine, to provide such innovative solutions. In order to explain specific physical difficulties, innovative lump periodic and analytical solutions have been investigated. These discoveries have been proven to be useful in the transmission of long-wave and high-power communications networks. It is important to highlight that the results given in thiswork depict new features and reflect previously unknown physical dynamics for the governing model.Article Citation - WoS: 19Citation - Scopus: 23Simulating the Joint Impact of Temporal and Spatial Memory Indices Via a Novel Analytical Scheme(Springer, 2021) Alquran, Marwan; Sivasundaram, Seenith; Baleanu, Dumitru; Jaradat, ImadThe prime concern of this study is to simulate the joint effect for the presence of two fractional derivative parameters (memory indices) by providing a novel analytical solution scheme for the fractional initial value problems. Our goal has been fulfilled by extending the residual power series method into the two-dimensional time and space, with time and space endowed with fractional derivative orders alpha and gamma, respectively (simply denoted by fractional (alpha,gamma) space), by virtue of a new (alpha,gamma)-fractional power series representation ((alpha,gamma)-FPS). The necessary theoretical framework for the convergence and the error bound is also provided to enrich our analytical study. Among other main findings, it is deserved to mention that the fractional derivative parameters act like the homotopy parameters, in a topological sense, to generate a rapidly convergent series solution for the classical integer version of the problem under consideration, which promotes the idea that these parameters describe a remnant memory. The efficiency of the proposed approach is assessed by projecting the obtained solutions of several well-known (non)linear problems into lower-dimensional fractal space and/or into integer space and then comparing them with the corresponding results of the literature. Overall, the method shows a wide versatility and adequacy in dealing with such hybrid problems.