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Öğe A method for solving the generalized Camassa-Choi problem with the Mittag-Leffler function and temporal local derivative(Elsevier, 2023) Hashemi, Mir Sajjad; Akguel, Ali; Hassan, Ahmed; Bayram, MustafaThis paper focuses on a reduction technique to discover exact solutions for the generalized Camassa-Choi equation with temporal local M-derivative. The paper presents various types of exact solutions along with their corresponding first integrals. Furthermore, the interactions between the orders of alpha and beta in the M-derivative are taken into account and depicted graphically for the derived solutions. Remarkably, the paper demonstrates that in certain situations, exact solutions can be obtained for any value of n, which holds significant mathematical intrigue. The authors note that Nucci's reduction technique has not previously been employed for differential equations with M-derivative, to the best of their knowledge.Öğe A new application of the Legendre reproducing kernel method(Amer Inst Mathematical Sciences-Aims, 2022) Foroutan, Mohammad Reza; Hashemi, Mir Sajjad; Gholizadeh, Leila; Akgul, Ali; Jarad, FahdIn this work, we apply the reproducing kernel method to coupled system of second and fourth order boundary value problems. We construct a novel algorithm to acquire the numerical results of the nonlinear boundary-value problems. We also use the Legendre polynomials. Additionally, we discuss the convergence analysis and error estimates. We demonstrate the numerical simulations to prove the efficiency of the presented method.Öğe Analytical treatment of the couple stress fluid-filled thin elastic tubes(Elsevier Gmbh, Urban & Fischer Verlag, 2017) Hashemi, Mir Sajjad; Inc, Mustafa; Akgul, AliIn this paper, we present the symmetries and self-adjointness of the problem about the couple stress fluid-filled thin elastic tubes. Some soliton solutions of the specified problem are constructed with the aid of Lie group symmetry method. (C) 2017 Elsevier GmbH. All rights reserved.Öğe Analytical treatment on the nonlinear Schriidinger equation with the parabolic law(Elsevier, 2023) Han, Xiang-Lin; Hashemi, Mir Sajjad; Samei, Mohammad Esmael; Akgul, Ali; El Din, Sayed M.The objective of this study is to investigate a few solutions to the nonlinear Schriidinger problem with parabolic law. The first integral and exact solutions for the reduced ODE of the model under consideration are extracted using Nucci's reduction approach. Finally, using the efficient and effective solutions technique, we display density plots and 2D, 3D plots for the suggested governing model.Öğe Fractal Fractional Order Operators in Computational Techniques for Mathematical Models in Epidemiology(Tech Science Press, 2024) Farman, Muhammad; Akgul, Ali; Hashemi, Mir Sajjad; Guran, Liliana; Bucur, AmeliaNew fractional operators, the COVID-19 model has been studied in this paper. By using different numerical techniques and the time fractional parameters, the mechanical characteristics of the fractional order model are identified. The uniqueness and existence have been established. The model's Ulam-Hyers stability analysis has been found. In order to justify the theoretical results, numerical simulations are carried out for the presented method in the range of fractional order to show the implications of fractional and fractal orders. We applied very effective numerical techniques to obtain the solutions of the model and simulations. Also, we present conditions of existence for a solution to the proposed epidemic model and to calculate the reproduction number in certain state conditions of the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered for analysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in the Community. For this reason, we employed the COVID-19 fractal fractional derivative model in the example of Wuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractional operators can facilitate the improvement of decision-making for measures to be taken in the management of an epidemic situation.Öğe Group preserving scheme and reproducing kernel method for the Poisson-Boltzmann equation for semiconductor devices(Springer, 2017) Akgul, Ali; Inc, Mustafa; Hashemi, Mir SajjadThis paper introduces that the nonlinear Poisson-Boltzmann equation for semiconductor devices describing potential distribution in a double-gate metal oxide semiconductor field effect transistor (DG-MOSFET) is exactly solvable. The DG-MOSFET shows one of the most advanced device structures in semiconductor technology and is a primary focus of modeling efforts in the semiconductor industry. Lie symmetry properties of this model is investigated in order to extract some exact solutions. The reproducing kernel Hilbert space method and group preserving scheme also have been applied to the nonlinear equation. Numerical results show that the present methods are very effective.Öğe NEW METHOD FOR INVESTIGATING THE DENSITY-DEPENDENT DIFFUSION NAGUMO EQUATION(Vinca Inst Nuclear Sci, 2018) Akgul, Ali; Hashemi, Mir Sajjad; Inc, Mustafa; Baleanu, Dumitru; Khan, HasibWe apply reproducing kernel method to the density-dependent diffusion Nagumo equation. Powerful method has been applied by reproducing kernel functions. The approximations to the exact solution are obtained. In particular, series solutions are obtained. These solutions demonstrate the certainty of the method The results acquired in this work conceive many attracted behaviors that assure further work on the Nagumo equation.Öğe New Solutions of Nonlinear Dispersive Equation in Higher-Dimensional Space with Three Types of Local Derivatives(Mdpi, 2022) Akgul, Ali; Hashemi, Mir Sajjad; Jarad, FahdThe aim of this paper is to use the Nucci's reduction method to obtain some novel exact solutions to the s-dimensional generalized nonlinear dispersive mK(m,n) equation. To the best of the authors' knowledge, this paper is the first work on the study of differential equations with local derivatives using the reduction technique. This higher-dimensional equation is considered with three types of local derivatives in the temporal sense. Different types of exact solutions in five cases are reported. Furthermore, with the help of the Maple package, the solutions found in this study are verified. Finally, several interesting 3D, 2D and density plots are demonstrated to visualize the nonlinear wave structures more efficiently.Öğe On new exact solutions of the generalized Fitzhugh-Nagumo equation with variable coefficients(Wiley, 2024) Hashemi, Mir Sajjad; Akgul, AliIn this article, Heir-equations method has been used to investigate nonclassical symmetries and new exact solutions of the generalized Fitzhugh-Nagumo equation with variable coefficients. Different types of variable coefficients with corresponding exact solutions have been considered.Öğe On solitons and invariant solutions of the Magneto-electro-elastic circular rod(Taylor & Francis Ltd, 2016) Hashemi, Mir Sajjad; Inc, Mustafa; Kilic, Bulent; Akgul, AliIn this paper, we study themagneto-electro-elastic (MEE) circular rod by the aid of Lie group symmetry method. Corresponding symmetry reductions of MEE and its some invariant solutions using the Nucci's method are completely considered too. Subsequently, the soliton solutions are obtained using the first integral method.Öğe On the solutions of boundary value problems(Ramazan Yaman, 2021) Akgul, Ali; Hashemi, Mir Sajjad; Seyfi, NegarWe investigate the nonlinear boundary value problems by reproducing kernel Hilbert space technique in this paper. We construct some reproducing kernel Hilbert spaces. We define a bounded linear operator to obtain the solutions of the problems. We demonstrate our numerical results by some tables. We com-pare our numerical results with some results exist in the literature to present the efficiency of the proposed method.Öğe Optical solitons with an extended (3+1)-dimensional nonlinear conformable Schrödinger equation including cubic–quintic nonlinearity(Elsevier B.V., 2023) Mirzazadeh, Mohammad; Sharif, A.; Hashemi, Mir Sajjad; Akgül, Ali; El Din, Sayed M.In this paper, we study the extended (3+1)-dimensional nonlinear conformable Schrödinger equation with cubic–quintic nonlinearity. We use three different methods to obtain exact solutions of this equation: the G?/G expansion method, the extended hyperbolic method, and Nucci's reduction method. We show that these methods are effective in finding solitary wave solutions, periodic wave solutions, and rational solutions of the equation. Besides, a first integral of the considered equation is derived by the Nucci reduction technique. Our results demonstrate the applicability of these methods in finding exact solutions to nonlinear PDEs, especially in cases where other methods are not effective. © 2023 The Author(s)Öğe Solving the Lane-Emden Equation within a Reproducing Kernel Method and Group Preserving Scheme(Mdpi, 2017) Hashemi, Mir Sajjad; Akgul, Ali; Inc, Mustafa; Mustafa, Idrees Sedeeq; Baleanu, DumitruWe apply the reproducing kernel method and group preserving scheme for investigating the Lane-Emden equation. The reproducing kernel method is implemented by the useful reproducing kernel functions and the numerical approximations are given. These approximations demonstrate the preciseness of the investigated techniques.
