Browsing by Author "Alquran, Marwan"

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Citation Count: Makhadmih, M.;...et.al. (2022). "A new analytical method to simulate the mutual impact of space-time memory indices embedded in (1+2)-physical models", Nonlinear Engineering, Vol.11, No.1, pp.522-538.
A new analytical method to simulate the mutual impact of space-time memory indices embedded in (1+2)-physical models
(2022) Makhadmih, M; Jaradat, I; Alquran, Marwan; Baleanu, Dumitru; 56389
In 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.
Citation Count: Alquran, M...et al. (2019). "An Analytical Study of (2 + 1)-Dimensional Physical Models Embedded Entirely in Fractal Space", Romanian Journal of Physics, Vol. 64, No. 1-2.
An Analytical Study of (2 + 1)-Dimensional Physical Models Embedded Entirely in Fractal Space
(Editura Academiei Romane, 2019) Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; Abdel-Muhsen, Ruwa; 56389
In this article, we analytically furnish the solution of (2+1)-dimension-al fractional differential equations, with distinct fractal-memory indices in all coordinates, as a trivariate (α, β, γ)−fractional power series representation. The method is tested on several physical models with inherited memories. Moreover, a version of Taylor’s theorem in fractal three-dimensional space is presented. As a special case, the solutions of the corresponding integer-order cases are extracted by letting α, β, γ → 1, which indicates to some extent for a sequential memory.
Citation Count: Alquran, Marwan...et al. (2019). "An Analytical Study of (2+1)-Dimensional Physical Models Embedded Entirely in Fractal Space", Romanian Journal of Physics, Vol. 64.
An Analytical Study of (2+1)-Dimensional Physical Models Embedded Entirely in Fractal Space
(Editura Academiei Romane, 2019) Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; Abdel-Muhsen, Ruwa; 56389
In this article, we analytically furnish the solution of (2 + 1)-dimensional fractional differential equations, with distinct fractal-memory indices in all coordinates, as a trivariate (alpha, beta, gamma)-fractional power series representation. The method is tested on several physical models with inherited memories. Moreover, a version of Taylor's theorem in fractal three-dimensional space is presented. As a special case, the solutions of the corresponding integer-order cases are extracted by letting alpha, beta, gamma -> 1, which indicates to some extent for a sequential memory.
Citation Count: Alquran, Marwan...et al. (2019). "AN ANALYTICAL STUDY OF (2+1)-DIMENSIONAL PHYSICAL MODELS EMBEDDED ENTIRELY IN FRACTAL SPACE", Romanian Journal of Physics, Vol. 64, No. 1-2.
AN ANALYTICAL STUDY OF (2+1)-DIMENSIONAL PHYSICAL MODELS EMBEDDED ENTIRELY IN FRACTAL SPACE
(2019) Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; Abdel-Muhsen, Ruwa; 56389
In this article, we analytically furnish the solution of (2 + 1)-dimensional fractional differential equations, with distinct fractal-memory indices in all coordinates, as a trivariate (alpha, beta, gamma)-fractional power series representation. The method is tested on several physical models with inherited memories. Moreover, a version of Taylor's theorem in fractal three-dimensional space is presented. As a special case, the solutions of the corresponding integer-order cases are extracted by letting alpha, beta, gamma -> 1, which indicates to some extent for a sequential memory.
Citation Count: Alquran, Marwan...et al. (2019). "AN ANALYTICAL STUDY OF (2+1)-DIMENSIONAL PHYSICAL MODELS EMBEDDED ENTIRELY IN FRACTAL SPACE", Romanian Journal of Physics, Vol. 64, No. 1-2.
AN ANALYTICAL STUDY OF (2+1)-DIMENSIONAL PHYSICAL MODELS EMBEDDED ENTIRELY IN FRACTAL SPACE
(2019) Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; Abdel-Muhsen, Ruwa; 56389
In this article, we analytically furnish the solution of (2 + 1)-dimensional fractional differential equations, with distinct fractal-memory indices in all coordinates, as a trivariate (alpha, beta, gamma)-fractional power series representation. The method is tested on several physical models with inherited memories. Moreover, a version of Taylor's theorem in fractal three-dimensional space is presented. As a special case, the solutions of the corresponding integer-order cases are extracted by letting alpha, beta, gamma -> 1, which indicates to some extent for a sequential memory.
Citation Count: Jaradat, I...et al. (2019). "An Avant-Garde Handling of Temporal-Spatial Fractional Physical Models", International Journal of Nonlinear Sciences and Numerical Simulation.
An Avant-Garde Handling of Temporal-Spatial Fractional Physical Models
(De Gruyter Open LTD, 2019) Jaradat, Imad; Alquran, Marwan; Katatbeh, Qutaibeh; Yousef, Feras; Momani, Shaher Mohammad; Baleanu, Dumitru; 56389
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 Count: Alquran, Marwan...et al. (2020). "CHAOTIC AND SOLITONIC SOLUTIONS FOR A NEW TIME-FRACTIONAL TWO-MODE KORTEWEG-DE VRIES EQUATION", Romanian Reports in Physics, Vol. 72, No. 3.
CHAOTIC AND SOLITONIC SOLUTIONS FOR A NEW TIME-FRACTIONAL TWO-MODE KORTEWEG-DE VRIES EQUATION
(2020) Alquran, Marwan; Jaradat, Imad; Momani, Shaher; Baleanu, Dumitru; 56389
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 Count: Ali, Mohammed ...et al. (2020). "DYNAMICS OF INTEGER-FRACTIONAL TIME-DERIVATIVE FOR THE NEW TWO-MODE KURAMOTO-SIVASHINSKY MODEL", Romanian Reports in Physics, Vol. 72, No. 1.
DYNAMICS OF INTEGER-FRACTIONAL TIME-DERIVATIVE FOR THE NEW TWO-MODE KURAMOTO-SIVASHINSKY MODEL
(2020) Ali, Mohammed; Alquran, Marwan; Jaradat, Imad; Abu Afouna, Nour; Baleanu, Dumitru; 56389
In 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.
Citation Count: Jaradat, Imad...et al. (2020). "Higher-dimensional physical models with multimemory indices: analytic solution and convergence analysis", Advances in Difference Equations, Vol. 2020, No. 1.
Higher-dimensional physical models with multimemory indices: analytic solution and convergence analysis
(2020) Jaradat, Imad; Alquran, Marwan; Abdel-Muhsen, Ruwa; Momani, Shaher; Baleanu, Dumitru; 56389
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 Count: Abu Irwaq, Issam...et al. (2018). New dual-mode Kadomtsev-Petviashvili model with strong-weak surface tension: analysis and application, Advances in Difference Equations.
New dual-mode Kadomtsev-Petviashvili model with strong-weak surface tension: analysis and application
(Pushpa Publishing House, 2018) Abu Irwaq, Issam; Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; 56389
Dual-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.
Citation Count: Yousef, Feras...et al. (2019). "New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices", Journal of Computational and Nonlinear Dynamics, Vol. 14, No. 11.
New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices
(2019) Yousef, Feras; Alquran, Marwan; Jaradat, Imad; Momani, Shaher; Baleanu, Dumitru; 56389
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 Count: Alquran, Marwan;...et.al. (2023). "Nonautonomous lump-periodic and analytical solutions to the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation", Nonlinear Dynamics, Vol.111, No.12, pp.11429-11436.
Nonautonomous lump-periodic and analytical solutions to the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation
(2023) Alquran, Marwan; Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, Dumitru; 56389
This 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 this work depict new features and reflect previously unknown physical dynamics for the governing model.
Citation Count: Alquran, Marwan...et al. (2023). "Nonautonomous lump-periodic and analytical solutions tothe (3+1)-dimensional generalized Kadomtsev-Petviashviliequation", NONLINEAR DYNAMICS, Vol. 111, No. 12, pp. 11429-11436.
Nonautonomous lump-periodic and analytical solutions tothe (3+1)-dimensional generalized Kadomtsev-Petviashviliequation
(2023) Alquran, Marwan; Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, Dumitru; 56389
This 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.
Citation Count: Jaradat, Imad...et al. (2020). "Numerical schemes for studying biomathematics model inherited with memory-time and delay-time", ALEXANDRIA ENGINEERING JOURNAL, Vol. 59, No.5, pp. 2969-2974.
Numerical schemes for studying biomathematics model inherited with memory-time and delay-time
(2020) Jaradat, Imad; Alquran, Marwan; Momani, Shaher; Baleanu, Dumitru; 56389
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 Count: Partohaghighi, Mohammad;...et.al. (2023). "Numerical simulation of the fractional diffusion equation", International Journal of Modern Physics B, Vol.37, No.10.
Numerical simulation of the fractional diffusion equation
(2023) Partohaghighi, Mohammad; Yusuf, Abdullahi; Jarad, Fahd; Sulaiman, Tukur A.; Alquran, Marwan; 234808
During 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.
Citation Count: Jaradat, Imad;...et.al. (2019). "On (2 + 1)-dimensional physical models endowed with decoupled spatial and temporal memory indices⋆", European Physical Journal Plus, Vol.134, No.7.
On (2 + 1)-dimensional physical models endowed with decoupled spatial and temporal memory indices⋆
(2019) Jaradat, Imad; Alquran, Marwan; Yousef, Feras; Momani, Shaher; Baleanu, Dumitru; 56389
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 (α, β) -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 (α, β) -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 (α, β) -models are solved and the presence of remnant memory, due to the fractional derivatives, is graphically illustrated.
Citation Count: Jaradat, Imad...et al. (2019). "On (2+1)-dimensional physical models endowed with decoupled spatial and temporal memory indices(star)", European Physical Journal Plus, Vol. 134, No. 7.
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
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 Count: Jaradat, Imad;...et.al. (2023). "Optical wave propagation to a nonlinear phenomenon with pulses in optical fiber", Optical and Quantum Electronics, Vol.55, no.4.
Optical wave propagation to a nonlinear phenomenon with pulses in optical fiber
(2023) Jaradat, Imad; Sulaiman, Tukur Abdulkadir; Alshomrani, Ali S.; Yusuf, Abdullahi; Alquran, Marwan; Baleanu, Dumitru; 56389
We 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.
Citation Count: Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru, "Shapes and dynamics of dual-mode Hirota-Satsuma coupled KdV equations: Exact traveling wave solutions and analysis", Chinese Journal of Physics, Vol. 58, pp. 49-56, (2019).
Shapes and dynamics of dual-mode Hirota-Satsuma coupled KdV equations: Exact traveling wave solutions and analysis
(Elsevier Science BV, 2019) Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; 56389
In this paper we communicated with three different ansatze methods including the tanh-expansion method, the rational sine-cosine method and the Kudryashov-expansion method to study solitary wave solutions for a new developed nonlinear equation. We presented new generalized Hirota-Satsuma coupled KdV system of second-order in time t involving phase-velocity, dispersion and nonlinearity parameters. The new system can be defined as a dual-mode model where each involved field-function possess a spreading of dual-waves instead of single-mode wave. Graphical illustrations on the effect of both phase-velocity and dispersion-nonlinearity factors on the spacing of the obtained dual-waves are provided.
Citation Count: Jaradat, Imad...et al. (2021). "Simulating the joint impact of temporal and spatial memory indices via a novel analytical scheme", NONLINEAR DYNAMICS, Vol. 103, No. 3, pp. 2509-2524.
Simulating the joint impact of temporal and spatial memory indices via a novel analytical scheme
(2021) Jaradat, Imad; Alquran, Marwan; Sivasundaram, Seenith; Baleanu, Dumitru; 56389
The 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.