Browsing by Author "Abu Arqub, Omar"

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Citation - WoS: 34
Citation - Scopus: 40
A Novel Analytical Algorithm for Generalized Fifth-Order Time-Fractional Nonlinear Evolution Equations With Conformable Time Derivative Arising in Shallow Water Waves
(Elsevier, 2022) Al-Smadi, Mohammed; Almusawa, Hassan; Baleanu, Dumitru; Hayat, Tasawar; Alhodaly, Mohammed; Osman, M. S.; Abu Arqub, Omar; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The purpose of this research is to study, investigate, and analyze a class of temporal time-FNEE models with time-FCDs that are indispensable in numerous nonlinear wave propagation phenomena. For this purpose, an efficient semi-analytical algorithm is developed and designed in view of the residual error terms for solving a class of fifth-order time-FCKdVEs. The analytical solutions of a dynamic wavefunction of the fractional Ito, Sawada-Kotera, Lax's Korteweg-de Vries, Caudrey-Dodd-Gibbon, and Kaup-Kupershmidt equations are provided in the form of a convergent conformable time-fractional series. The related consequences are discussed both theoretically as well as numerically considering the conformable sense. In this direction, convergence analysis and error estimates of the developed algorithm are studied and analyzed as well. Concerning the considered models, specific unidirectional physical experiments are given in a finite compact regime to confirm the theoretical aspects and to demonstrate the superiority of the novel algorithm compared to the other existing numerical methods. Moreover, some representative results are presented in two- and three-dimensional graphs, whilst dynamic behaviors of fractional parameters are reported for several alpha values. From the practical viewpoint, the archived simulations and consequences justify that the iterative algorithm is a straightforward and appropriate tool with computational efficiency for long-wavelength solutions of nonlinear time-FPDEs in physical phenomena. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University
Citation - WoS: 118
Citation - Scopus: 130
A Novel Expansion Iterative Method for Solving Linear Partial Differential Equations of Fractional Order
(Elsevier Science inc, 2015) Abu Arqub, Omar; Momani, Shaher; Baleanu, Dumitru; Alsaedi, Ahmed; El-Ajou, Ahmad; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this manuscript, we implement a relatively new analytic iterative technique for solving time-space-fractional linear partial differential equations subject to given constraints conditions based on the generalized Taylor series formula. The solution methodology is based on generating the multiple fractional power series expansion solution in the form of a rapidly convergent series with minimum size of calculations. This method can be used as an alternative to obtain analytic solutions of different types of fractional linear partial differential equations applied in mathematics, physics, and engineering. Some numerical test applications were analyzed to illustrate the procedure and to confirm the performance of the proposed method in order to show its potentiality, generality, and accuracy for solving such equations with different constraints conditions. Numerical results coupled with graphical representations explicitly reveal the complete reliability and efficiency of the suggested algorithm. (C) 2015 Elsevier Inc. All rights reserved.
Citation - WoS: 30
Citation - Scopus: 48
A Numerical Combined Algorithm in Cubic B-Spline Method and Finite Difference Technique for the Time-Fractional Nonlinear Diffusion Wave Equation With Reaction and Damping Terms
(Elsevier, 2022) Abu Arqub, Omar; Tayebi, Soumia; Baleanu, Dumitru; Osman, M. S.; Mahmoud, W.; Alsulami, Hamed; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The applications of the diffusion wave model of a time-fractional kind with damping and reaction terms can occur within classical physics. This quantification of the activity can measure the diagnosis of mechanical waves and light waves. The goal of this work is to predict and construct numerical solutions for such a diffusion model based on the uniform cubic B-spline functions. The Caputo time-fractional derivative has been estimated using the standard finite difference technique, whilst, the uniform cubic B-spline functions have been employed to achieve spatial discretization. The convergence of the suggested blueprint is discussed in detail. To assert the efficiency and authenticity of the study, we compute the approximate solutions for a couple of applications of the diffusion model in electromagnetics and fluid dynamics. To show the mathematical simulation, several tables and graphs are shown, and it was found that the graphical representations and their physical explanations describe the behavior of the solutions lucidly. The key benefit of the resultant scheme is that the algorithm is straightforward and makes it simple to implement as utilized in the highlight and conclusion part.