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Search Results (5)

Search Parameters:
Keywords = Daftardar-Gejji and Jafari method

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20 pages, 691 KiB  
Article
An Analysis of the Effects of Lifestyle Changes by Using a Fractional-Order Population Model of the Overweight/Obese Diabetic Population
by Kholoud Saad Albalawi, Kuldeep Malik, Badr Saad T. Alkahtani and Pranay Goswami
Fractal Fract. 2023, 7(12), 839; https://doi.org/10.3390/fractalfract7120839 - 27 Nov 2023
Cited by 3 | Viewed by 1380
Abstract
Unbalanced lifestyles and other underlying medical conditions are responsible for the worrying pace at which diabetes mellitus is becoming a global health crisis. Recent studies suggest that placing a diabetic patient into remission through a rigorous lifestyle change program can normalize blood glucose [...] Read more.
Unbalanced lifestyles and other underlying medical conditions are responsible for the worrying pace at which diabetes mellitus is becoming a global health crisis. Recent studies suggest that placing a diabetic patient into remission through a rigorous lifestyle change program can normalize blood glucose levels. This research focuses on fractional order derivative-based mathematical modeling and analysis of the diabetes mellitus model with remission parameters. Firstly, the existence and uniqueness of the solution of the diabetes mellitus model are discussed. Non-negativity and boundedness are also examined. Afterward, the concept of the Jacobian matrix is used to investigate the stability of the model’s equilibrium points. The Daftardar-Gejji and Jafari Method has finally been applied to approximate the solutions. The conclusions drawn from numerical simulations of the diabetic model with fractional-order derivatives show a clear dependence on the remission parameters and fractional-order derivative. Full article
(This article belongs to the Special Issue Feature Papers for Mathematical Physics Section)
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26 pages, 378 KiB  
Article
Some New Quantum Numerical Techniques for Solving Nonlinear Equations
by Kamsing Nonlaopon, Awais Gul Khan, Farah Ameen, Muhammad Uzair Awan and Clemente Cesarano
Symmetry 2022, 14(9), 1829; https://doi.org/10.3390/sym14091829 - 3 Sep 2022
Cited by 4 | Viewed by 1660
Abstract
In this paper, we introduce some new quantum numerical techniques of midpoint and trapezoidal type essentially by using the decomposition technique. We also check the order of convergence of our suggested iterative methods. Numerical examples demonstrate that the new q-iterative methods can [...] Read more.
In this paper, we introduce some new quantum numerical techniques of midpoint and trapezoidal type essentially by using the decomposition technique. We also check the order of convergence of our suggested iterative methods. Numerical examples demonstrate that the new q-iterative methods can generate solutions to the nonlinear equations with acceptable accuracy. Full article
8 pages, 1116 KiB  
Article
New Solution of the Sine-Gordon Equation by the Daftardar-Gejji and Jafari Method
by Belal Batiha
Symmetry 2022, 14(1), 57; https://doi.org/10.3390/sym14010057 - 2 Jan 2022
Cited by 21 | Viewed by 2157
Abstract
In this article, the Daftardar-Gejji and Jafari method (DJM) is used to obtain an approximate analytical solution of the sine-Gordon equation. Some examples are solved to demonstrate the accuracy of DJM. A comparison study between DJM, the variational iteration method (VIM), and the [...] Read more.
In this article, the Daftardar-Gejji and Jafari method (DJM) is used to obtain an approximate analytical solution of the sine-Gordon equation. Some examples are solved to demonstrate the accuracy of DJM. A comparison study between DJM, the variational iteration method (VIM), and the exact solution are presented. The comparison of the present symmetrical results with the existing literature is satisfactory. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear and Convex Analysis)
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17 pages, 355 KiB  
Article
On Iterative Methods for Solving Nonlinear Equations in Quantum Calculus
by Gul Sana, Pshtiwan Othman Mohammed, Dong Yun Shin, Muhmmad Aslam Noor and Mohammad Salem Oudat
Fractal Fract. 2021, 5(3), 60; https://doi.org/10.3390/fractalfract5030060 - 25 Jun 2021
Cited by 18 | Viewed by 3361
Abstract
Quantum calculus (also known as the q-calculus) is a technique that is similar to traditional calculus, but focuses on the concept of deriving q-analogous results without the use of the limits. In this paper, we suggest and analyze some new q [...] Read more.
Quantum calculus (also known as the q-calculus) is a technique that is similar to traditional calculus, but focuses on the concept of deriving q-analogous results without the use of the limits. In this paper, we suggest and analyze some new q-iterative methods by using the q-analogue of the Taylor’s series and the coupled system technique. In the domain of q-calculus, we determine the convergence of our proposed q-algorithms. Numerical examples demonstrate that the new q-iterative methods can generate solutions to the nonlinear equations with acceptable accuracy. These newly established methods also exhibit predictability. Furthermore, an analogy is settled between the well known classical methods and our proposed q-Iterative methods. Full article
(This article belongs to the Special Issue Operators of Fractional Calculus and Their Multidisciplinary Applications)
10 pages, 2147 KiB  
Article
Exact Solution of Ambartsumian Delay Differential Equation and Comparison with Daftardar-Gejji and Jafari Approximate Method
by Huda O. Bakodah and Abdelhalim Ebaid
Mathematics 2018, 6(12), 331; https://doi.org/10.3390/math6120331 - 17 Dec 2018
Cited by 38 | Viewed by 3345
Abstract
The Ambartsumian equation, a linear differential equation involving a proportional delay term, is used in the theory of surface brightness in the Milky Way. In this paper, the Laplace-transform was first applied to this equation, and then the decomposition method was implemented to [...] Read more.
The Ambartsumian equation, a linear differential equation involving a proportional delay term, is used in the theory of surface brightness in the Milky Way. In this paper, the Laplace-transform was first applied to this equation, and then the decomposition method was implemented to establish a closed-form solution. The present closed-form solution is reported for the first time for the Ambartsumian equation. Numerically, the calculations have demonstrated a rapid rate of convergence of the obtained approximate solutions, which are displayed in several graphs. It has also been shown that only a few terms of the new approximate solution were sufficient to achieve extremely accurate numerical results. Furthermore, comparisons of the present results with the existing methods in the literature were introduced. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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