Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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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: 12Citation - Scopus: 13Numerical Schemes for Studying Biomathematics Model Inherited With Memory-Time and Delay-Time(Elsevier, 2020) Alquran, Marwan; Momani, Shaher; Baleanu, Dumitru; Jaradat, ImadThe effect of inherited memory-time and delay-time in the formulation of a mathematical population growth model is considered. Two different numerical schemes are introduced to study analytically the propagation of population growth. We provide a graphical analysis that shows the impact of both memory-time and delay-time acting on the behavior of population density. We concluded that both delay-time and time-fractional-derivative play the same role as delaying the propagation of the nonlinear population growth. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.Article Citation - WoS: 1Citation - Scopus: 2Higher-Dimensional Physical Models With Multimemory Indices: Analytic Solution and Convergence Analysis(Springer, 2020) Alquran, Marwan; Abdel-Muhsen, Ruwa; Momani, Shaher; Baleanu, Dumitru; Jaradat, ImadThe purpose of this work is to analytically simulate the mutual impact for the existence of both temporal and spatial Caputo fractional derivative parameters in higher-dimensional physical models. For this purpose, we employ the gamma_-Maclaurin series along with an amendment of the power series technique. To supplement our idea, we present the necessary convergence analysis regarding the gamma_-Maclaurin series. As for the application side, we solved versions of the higher-dimensional heat and wave models with spatial and temporal Caputo fractional derivatives in terms of a rapidly convergent gamma_-Maclaurin series. The method performed extremely well, and the projections of the obtained solutions into the integer space are compatible with solutions available in the literature. Finally, the graphical analysis showed a possibility that the Caputo fractional derivatives reflect some memory characteristics.Article Citation - WoS: 25Citation - Scopus: 32Ternary-Fractional Differential Transform Schema: Theory and Application(Springer, 2019) Alquran, Marwan; Jaradat, Imad; Momani, Shaher; Baleanu, Dumitru; Yousef, FerasIn this article, we propose a novel fractional generalization of the three-dimensional differential transform method, namely the ternary-fractional differential transform method, that extends its applicability to encompass initial value problems in the fractal 3D space. Several illustrative applications, including the Schrodinger, wave, Klein-Gordon, telegraph, and Burgers' models that are fully embedded in the fractal 3D space, are considered to demonstrate the superiority of the proposed method compared with other generalized methods in the literature. The obtained solution is expressed in a form of an (alpha) over bar -fractional power series, with easily computed coefficients, that converges rapidly to its closed-form solution. Moreover, the projection of the solutions into the integer 3D space corresponds with the solutions of the classical copies for these models. This reveals that the suggested technique is effective and accurate for handling many other linear and nonlinear models in the fractal 3D space. Thus, research on this trend is worth tracking.Article Citation - WoS: 22Citation - Scopus: 24Stationary Wave Solutions for New Developed Two-waves' Fifth-Order Korteweg-De Vries Equation(Springeropen, 2019) Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; Ali, MohammedIn 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.Article Citation - WoS: 24Citation - Scopus: 31New Dual-Mode Kadomtsev-Petviashvili Model With Strong-Weak Surface Tension: Analysis and Application(Pushpa Publishing House, 2018) Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; Abu Irwaq, IssamDual-mode (2 + 1)-dimensional Kadomtsev-Petviashvili (DMKP) equation is a new model which represents the spread of two simultaneously directional waves due to the involved term " utt (x, y, t)" in its equation. We present the construction of DMKP and search for possible solutions. The innovative tanh-expansion method and Kudryashov technique will be utilized to find the necessary constraint conditions which guarantee the existence of soliton solutions to DMKP. Supportive 3D plots will be provided to validate our findings.