Yazar "Nonlaopon, Kamsing" seçeneğine göre listele

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    A Caputo-Fabrizio fractional-order cholera model and its sensitivity analysis
    (2023) Ahmed, Idris; Akgül, Ali; Jarad, Fahd; Kumam, Poom; Nonlaopon, Kamsing
    In recent years, the availability of advanced computational techniques has led to a growing emphasis on fractional-order derivatives. This development has enabled researchers to explore the intricate dynamics of various biological models by employing fractional-order derivatives instead of traditional integer-order derivatives. This paper proposes a Caputo-Fabrizio fractional-order cholera epidemic model. Fixed-point theorems are utilized to investigate the existence and uniqueness of solutions. A recent and effective numerical scheme is employed to demonstrate the model's complex behaviors and highlight the advantages of fractional-order derivatives. Additionally, a sensitivity analysis is conducted to identify the most influential parameters.
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    Analysis of fractal fractional Lorenz type and financial chaotic systems with exponential decay kernels
    (Amer Inst Mathematical Sciences-Aims, 2022) Ul Haq, Ihtisham; Ahmad, Shabir; Saifullah, Sayed; Nonlaopon, Kamsing; Akgul, Ali
    In this work, we formulate a fractal fractional chaotic system with cubic and quadratic nonlinearities. A fractal fractional chaotic Lorenz type and financial systems are studied using the Caputo Fabrizo (CF) fractal fractional derivative. This study focuses on the characterization of the chaotic nature, and the effects of the fractal fractional-order derivative in the CF sense on the evolution and behavior of each proposed systems. The stability of the equilibrium points for the both systems are investigated using the Routh-Hurwitz criterion. The numerical scheme, which includes the discretization of the CF fractal-fractional derivative, is used to depict the phase portraits of the fractal fractional chaotic Lorenz system and the fractal fractional-order financial system. The simulation results presented in both cases include the two- and three-dimensional phase portraits to evaluate the applications of the proposed operators.
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    Analysis of Kink Behaviour of KdV-mKdV Equation under Caputo Fractional Operator with Non-Singular Kernel
    (Mdpi, 2022) Ali, Sajjad; Ullah, Aman; Ahmad, Shabir; Nonlaopon, Kamsing; Akgul, Ali
    The KdV equation has many applications in mechanics and wave dynamics. Therefore, researchers are carrying out work to develop and analyze modified and generalized forms of the standard KdV equation. In this paper, we inspect the KdV-mKdV equation, which is a modified and generalized form of the ordinary KdV equation. We use the fractional operator in the Caputo sense to analyze the equation. We examine some theoretical results concerned with the solution's existence, uniqueness, and stability. We employ a modified Laplace method to extract the numerical results of the considered equation. We use MATLAB-2020 to simulate the results in a few fractional orders. We report the effects of the fractional order on the wave dynamics of the proposed equation.
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    Bright Soliton Behaviours of Fractal Fractional Nonlinear Good Boussinesq Equation with Nonsingular Kernels
    (Mdpi, 2022) Sadiq, Gulaly; Ali, Amir; Ahmad, Shabir; Nonlaopon, Kamsing; Akgul, Ali
    In this manuscript, we investigate the nonlinear Boussinesq equation (BEQ) under fractal-fractional derivatives in the sense of the Caputo-Fabrizio and Atangana-Baleanu operators. We use the double modified Laplace transform (LT) method to determine the general series solution of the Boussinesq equation. We study the convergence, existence, uniqueness, boundedness, and stability of the solution of the considered good BEQ under the aforementioned derivatives. The obtained solutions are presented with numerical illustrations considering a particular example by two cases based on both derivatives with suitable initial conditions. The results are illustrated graphically where good agreements are obtained. Our results show that fractal-fractional derivatives are a very effective tool for studying nonlinear systems. Furthermore, when t increases, the solitary waves of the system oscillate. As the fractional order a or fractal dimension beta increases, the soliton solutions become coherently close to the exact solution. For compactness, an error analysis is performed. The absolute error reveals an approximate linear evolution in the soliton solutions as time increases and that the system does not blow up nonlinearly.
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    Nonlinear Schrodinger equation under non-singular fractional operators: A computational study
    (Elsevier, 2022) Khan, Asif; Ali, Amir; Ahmad, Shabir; Saifullah, Sayed; Nonlaopon, Kamsing; Akgul, Ali
    In this article, we present study on time fractional nonlinear Schrodinger equation. We investigate the behaviour of the aforesaid equation in two numerous types of operators having non-singular kernels, which are Atangana-Baleanu and Caputo-Fabrizio operators both considered in Caputo's sense. The considered operators are very useful as they present tremendous dynamics of the suggested equation. We obtain numerical and analytical solutions of the proposed equation under the aforementioned fractional operators by modified double Laplace transform. We present the error analysis of the suggested scheme, where we observed that the considered system primarily depend on time. When time is small, we obtain very small error between the exact and approximate solutions. For the efficiency of our considered scheme, we present some examples. Further, we present the graphical and numerical analysis of the scheme used for the solution.
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    Numerical Analysis of Time-Fractional Diffusion Equations via a Novel Approach
    (Hindawi Ltd, 2021) Shah, Nehad Ali; Saleem, S.; Akgul, Ali; Nonlaopon, Kamsing; Chung, Jae Dong
    The aim of this paper is a new semianalytical technique called the variational iteration transform method for solving fractional-order diffusion equations. In the variational iteration technique, identifying of the Lagrange multiplier is an essential rule, and variational theory is commonly used for this purpose. The current technique has the edge over other methods as it does not need extra parameters and polynomials. The validity of the proposed method is verified by considering some numerical problems. The solution achieved has shown that the better accuracy of the proposed technique. This paper proposes a simpler method to calculate the multiplier using the Shehu transformation, making a valuable technique to researchers dealing with various linear and nonlinear problems.