Browsing by Author "Jassim, Hassan Kamil"

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Citation - WoS: 27
Citation - Scopus: 50
Approximate Analytical Solutions of Goursat Problem Within Local Fractional Operators
(int Scientific Research Publications, 2016) Jassim, Hassan Kamil; Al Qurashi, Maysaa; Baleanu, Dumitru
The local fractional differential transform method (LFDTM) and local fractional decomposition method (LFDM) are applied to implement the homogeneous and nonhomogeneous Goursat problem involving local fractional derivative operators. The approximate analytical solution of this problem is calculated in form of a series with easily computable components. Examples are studied in order to show the accuracy and reliability of presented methods. We demonstrate that the two approaches are very effective and convenient for finding the analytical solutions of partial differential equations with local fractional derivative operators. (C) 2016 All rights reserved.
Citation - WoS: 22
Citation - Scopus: 48
Approximate Solutions of the Damped Wave Equation and Dissipative Wave Equation in Fractal Strings
(Mdpi, 2019) Jassim, Hassan Kamil; Baleanu, Dumitru
In this paper, we apply the local fractional Laplace variational iteration method (LFLVIM) and the local fractional Laplace decomposition method (LFLDM) to obtain approximate solutions for solving the damped wave equation and dissipative wave equation within local fractional derivative operators (LFDOs). The efficiency of the considered methods are illustrated by some examples. The results obtained by LFLVIM and LFLDM are compared with the results obtained by LFVIM. The results reveal that the suggested algorithms are very effective and simple, and can be applied for linear and nonlinear problems in sciences and engineering.
Citation - WoS: 27
Citation - Scopus: 56
Exact Solution of Two-Dimensional Fractional Partial Differential Equations
(Mdpi, 2020) Jassim, Hassan Kamil; Baleanu, Dumitru
In this study, we examine adapting and using the Sumudu decomposition method (SDM) as a way to find approximate solutions to two-dimensional fractional partial differential equations and propose a numerical algorithm for solving fractional Riccati equation. This method is a combination of the Sumudu transform method and decomposition method. The fractional derivative is described in the Caputo sense. The results obtained show that the approach is easy to implement and accurate when applied to various fractional differential equations.
Citation - WoS: 24
Citation - Scopus: 64
A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets
(Mdpi, 2019) Jassim, Hassan Kamil; Baleanu, Dumitru
In this paper, we apply a new technique, namely, the local fractional Laplace homotopy perturbation method (LFLHPM), on Helmholtz and coupled Helmholtz equations to obtain analytical approximate solutions. The iteration procedure is based on local fractional derivative operators (LFDOs). This method is a combination of the local fractional Laplace transform (LFLT) and the homotopy perturbation method (HPM). The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
Citation - WoS: 55
Citation - Scopus: 84
A Modification Fractional Variational Iteration Method for Solving Non-Linear Gas Dynamic and Coupled Kdv Equations Involving Local Fractional Operators
(Vinca inst Nuclear Sci, 2018) Jassim, Hassan Kamil; Khan, Hasib; Baleanu, Dumitru
In this paper, we apply a new technique, namely local fractional variational iteration transform method on homogeneous/non-homogeneous non-linear gas dynamic and coupled KdV equations to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative and integral operators. This method is the combination of the local fractional Laplace transform and variational iteration method. The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
Citation - WoS: 30
Citation - Scopus: 51
A Novel Approach for Korteweg-De Vries Equation of Fractional Order
(Shahid Chamran Univ Ahvaz, Iran, 2019) Baleanu, Dumitru; Jassim, Hassan Kamil
In this study, the local fractional variational iteration method (LFVIM) and the local fractional series expansion method (LFSEM) are utilized to obtain approximate solutions for Korteweg-de Vries equation (KdVE) within local fractional derivative operators (LFDOs). The efficiency of the considered methods is illustrated by some examples. The results reveal that the suggested algorithms are very effective and simple and can be applied for linear and nonlinear problems in mathematical physics.
Citation - WoS: 32
Citation - Scopus: 49
On the Approximate Solutions for a System of Coupled Korteweg-De Vries Equations With Local Fractional Derivative
(World Scientific Publ Co Pte Ltd, 2021) Jassim, Hassan Kamil; Baleanu, Dumitru; Chu, Yu-ming; Jafari, Hossein
In this paper, we utilize local fractional reduced differential transform (LFRDTM) and local fractional Laplace variational iteration methods (LFLVIM) to obtain approximate solutions for coupled KdV equations. The obtained results by both presented methods (the LFRDTM and the LFLVIM) are compared together. The results clearly show that those suggested algorithms are suitable and effective to handle linear and as well as nonlinear problems in engineering and sciences.
Citation - WoS: 27
Citation - Scopus: 61
On the Approximate Solutions of Local Fractional Differential Equations With Local Fractional Operators
(Mdpi, 2016) Tchier, Fairouz; Baleanu, Dumitru; Jafari, Hossein; Jassim, Hassan Kamil
In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods.
Citation - WoS: 15
Citation - Scopus: 31
On the Existence and Uniqueness of Solutions for Local Fractional Differential Equations
(Mdpi, 2016) Baleanu, Dumitru; Jafari, Hossein; Jassim, Hassan Kamil; Al Qurashi, Maysaa; Qurashi, Maysaa Al
In this manuscript, we prove the existence and uniqueness of solutions for local fractional differential equations (LFDEs) with local fractional derivative operators (LFDOs). By using the contracting mapping theorem (CMT) and increasing and decreasing theorem (IDT), existence and uniqueness results are obtained. Some examples are presented to illustrate the validity of our results.
Citation - WoS: 34
Citation - Scopus: 60
Solving Helmholtz Equation With Local Fractional Derivative Operators
(Mdpi, 2019) Jassim, Hassan Kamil; Al Qurashi, Maysaa; Baleanu, Dumitru
The paper presents a new analytical method called the local fractional Laplace variational iteration method (LFLVIM), which is a combination of the local fractional Laplace transform (LFLT) and the local fractional variational iteration method (LFVIM), for solving the two-dimensional Helmholtz and coupled Helmholtz equations with local fractional derivative operators (LFDOs). The operators are taken in the local fractional sense. Two test problems are presented to demonstrate the efficiency and the accuracy of the proposed method. The approximate solutions obtained are compared with the results obtained by the local fractional Laplace decomposition method (LFLDM). The results reveal that the LFLVIM is very effective and convenient to solve linear and nonlinear PDEs.