Yazar "Shah, Nehad Ali" seçeneğine göre listele

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    Analysis of Fractional-Order Regularized Long-Wave Models via a Novel Transform
    (Hindawi Ltd, 2022) Shah, Nehad Ali; El-Zahar, Essam R.; Akgul, Ali; Khan, Adnan; Kafle, Jeevan
    A new integral transform method for regularized long-wave (RLW) models having fractional-order is presented in this study. Although analytical approaches are challenging to apply to such models, semianalytical or numerical techniques have received much attention in the literature. We propose a new technique combining integral transformation, the Elzaki transform (ET), and apply it to regularized long-wave equations in this study. The RLW equations describe ion-acoustic waves in plasma and shallow water waves in seas. The results obtained are extremely important and necessary for describing various physical phenomena. This work considers an up-to-date approach and fractional operators in this context to obtain satisfactory approximate solutions to the proposed problems. We first define the Elzaki transforms of the Caputo fractional derivative (CFD) and Atangana-Baleanu fractional derivative (ABFD) and implement them for solving RLW equations. We can readily obtain numerical results that provide us with improved approximations after only a few iterations. The derived solutions were found to be in close contact with the exact solutions. Furthermore, the suggested procedure has attained the best level of accuracy. In fact, when compared to other analytical techniques for solving nonlinear fractional partial differential equations, the present method might be considered one of the finest.
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    NUMERICAL ANALYSIS OF FRACTIONAL-ORDER EMDEN-FOWLER EQUATIONS USING MODIFIED VARIATIONAL ITERATION METHOD
    (World Scientific Publ Co Pte Ltd, 2023) Zhang, Ri; Shah, Nehad Ali; El-Zahar, Essam R.; Akgul, Ali; Chung, Jae Dong
    This work aims at a new semi-analytical method called the variational iteration transform method for investigating fractional-order Emden-Fowler equations. The Shehu transformation and the iterative method are applied to achieve the solution of the given problems. The proposed method has the edge over other techniques as it does not required extra calculations. Some numerical problems are used to test the validity of the suggested method. The solution obtained has demonstrated that the proposed technique has a higher level of accuracy. The proposed method is capable of tackling various nonlinear fractional-order problems due to its simple implementation.
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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.
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    Numerical study of a nonlinear fractional chaotic Chua's circuit
    (Amer Inst Mathematical Sciences-Aims, 2023) Shah, Nehad Ali; Ahmed, Iftikhar; Asogwa, Kanayo K.; Zafar, Azhar Ali; Weera, Wajaree; Akgul, Ali
    As an exponentially growing sensitivity to modest perturbations, chaos is pervasive in nature. Chaos is expected to provide a variety of functional purposes in both technological and biological systems. This work applies the time-fractional Caputo and Caputo-Fabrizio fractional derivatives to the Chua type nonlinear chaotic systems. A numerical analysis of the mathematical models is used to compare the chaotic behavior of systems with differential operators of integer order versus systems with fractional differential operators. Even though the chaotic behavior of the classical Chua's circuit has been extensively investigated, our generalization can highlight new aspects of system behavior and the effects of memory on the evolution of the chaotic generalized circuit.