Browsing by Author "Momani, Shaher"

Now showing 1 - 12 of 12

Citation - WoS: 22
Citation - Scopus: 26
A nonstandard finite difference scheme for two-sided space-fractional partial differential equations
(World Scientific Publ Co Pte Ltd, 2012) Momani, Shaher; Baleanu, Dumitru; Abu Rqayiq, Abdullah; Baleanu, Dumitru; Matematik
In this paper, we apply the Mickens nonstandard discretization method to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain, and thereby increase the accuracy of the solutions. We examine the case when a left-handed and a right-handed fractional spatial derivative may be present in the partial differential equation. Two numerical examples using this method are presented and compared successfully with the exact analytical solutions.
Citation - WoS: 117
Citation - Scopus: 128
A novel expansion iterative method for solving linear partial differential equations of fractional order
(Elsevier Science inc, 2015) El-Ajou, Ahmad; Baleanu, Dumitru; Abu Arqub, Omar; Momani, Shaher; Baleanu, Dumitru; Alsaedi, Ahmed; Matematik
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: 12
Citation - Scopus: 16
An Avant-Garde Handling of Temporal-Spatial Fractional Physical Models
(Walter de Gruyter Gmbh, 2020) Jaradat, Imad; Baleanu, Dumitru; Alquran, Marwan; Katatbeh, Qutaibeh; Yousef, Feras; Momani, Shaher; Baleanu, Dumitru; 56389; Matematik
In 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.
Citation - WoS: 23
Citation - Scopus: 25
CHAOTIC 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; 56389; Matematik
The 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.
Citation - WoS: 1
Citation - Scopus: 2
Higher-dimensional physical models with multimemory indices: analytic solution and convergence analysis
(Springer, 2020) Jaradat, Imad; Baleanu, Dumitru; Alquran, Marwan; Abdel-Muhsen, Ruwa; Momani, Shaher; Baleanu, Dumitru; 56389; Matematik
The 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.
Citation - WoS: 3
Citation - Scopus: 4
HYPERCHAOTIC DYNAMICS of A NEW FRACTIONAL DISCRETE-TIME SYSTEM
(World Scientific Publ Co Pte Ltd, 2021) Khennaoui, Amina-Aicha; Baleanu, Dumitru; Ouannas, Adel; Momani, Shaher; Dibi, Zohir; Grassi, Giuseppe; Baleanu, Dumitru; Viet-Thanh Pham; 56389; Matematik
In recent years, some efforts have been devoted to nonlinear dynamics of fractional discrete-time systems. A number of papers have so far discussed results related to the presence of chaos in fractional maps. However, less results have been published to date regarding the presence of hyperchaos in fractional discrete-time systems. This paper aims to bridge the gap by introducing a new three-dimensional fractional map that shows, for the first time, complex hyperchaotic behaviors. A detailed analysis of the map dynamics is conducted via computation of Lyapunov exponents, bifurcation diagrams, phase portraits, approximated entropy and C-0 complexity. Simulation results confirm the effectiveness of the approach illustrated herein.
Citation - WoS: 15
Citation - Scopus: 18
New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices
(Asme, 2019) Yousef, Feras; Baleanu, Dumitru; Alquran, Marwan; Jaradat, Imad; Momani, Shaher; Baleanu, Dumitru; 56389; Matematik
Herein, 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.
Citation - WoS: 12
Citation - Scopus: 13
Numerical schemes for studying biomathematics model inherited with memory-time and delay-time
(Elsevier, 2020) Jaradat, Imad; Baleanu, Dumitru; Alquran, Marwan; Momani, Shaher; Baleanu, Dumitru; 56389; Matematik
The 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.
Citation - WoS: 14
Citation - Scopus: 17
On (2 + 1)-dimensional physical models endowed with decoupled spatial and temporal memory indices⋆
(Springer Heidelberg, 2019) Jaradat, Imad; Baleanu, Dumitru; Alquran, Marwan; Yousef, Feras; Momani, Shaher; Baleanu, Dumitru; 56389; Matematik
.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.
On (2+1)-dimensional physical models endowed with decoupled spatial and temporal memory indices(star)
(Springer Heidelberg, 2019) Baleanu, Dumitru; Jaradat, Imad; Alquran, Marwan; Yousef, Feras; Momani, Shaher; 56389; Matematik
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.
Citation - WoS: 63
Citation - Scopus: 75
Structure of optical soliton solution for nonliear resonant space-time Schrödinger equation in conformable sense with full nonlinearity term
(Iop Publishing Ltd, 2020) Alabedalhadi, Mohammed; Baleanu, Dumitru; Al-Smadi, Mohammed; Al-Omari, Shrideh; Baleanu, Dumitru; Momani, Shaher; 56389; Matematik
Nonclassical quantum mechanics along with dispersive interactions of free particles, long-range boson stars, hydrodynamics, harmonic oscillator, shallow-water waves, and quantum condensates can be modeled via the nonlinear fractional Schrodinger equation. In this paper, various types of optical soliton wave solutions are investigated for perturbed, conformable space-time fractional Schrodinger model competed with a weakly nonlocal term. The fractional derivatives are described by means of conformable space-time fractional sense. Two different types of nonlinearity are discussed based on Kerr and dual power laws for the proposed fractional complex system. The method employed for solving the nonlinear fractional resonant Schrodinger model is the hyperbolic function method utilizing some fractional complex transformations. Several types of exact analytical solutions are obtained, including bright, dark, singular dual-power-type soliton and singular Kerr-type soliton solutions. Moreover, some graphical simulations of those solutions are provided for understanding the physical phenomena.
Citation - WoS: 25
Citation - Scopus: 32
Ternary-fractional differential transform schema: theory and application
(Springer, 2019) Yousef, Feras; Baleanu, Dumitru; Alquran, Marwan; Jaradat, Imad; Momani, Shaher; Baleanu, Dumitru; 56389; Matematik
In 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.