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    Öğe
    A hybrid approach for non-linear fractional Newell-Whitehead-Segel model
    (Elsevier, 2024) Yadav, L. K.; Agarwal, G.; Gour, M. M.; Akguel, A.; Misro, Md Yushalify; Purohit, S. D.
    In this article, we applied the Shehu transform decomposition method (STDM) to obtain the approximate solution of the nonlinear fractional Newell-Whitehead-Segel equation that arises in various physical phenomena, such as fluid mechanics, solid -state physics, optics, plasma physics, dispersion, and chemical kinetics. The fractional NWS model is associated with the temperature and thermal convection of fluid dynamics, aiding in describing the formulation process on liquid surfaces restricted along a horizontally well-conducting boundary. To minimize computing complexity and intricacy, we utilized the proposed method, which combines the Shehu transform and the Adomian decomposition method, to solve the presented model. The results obtained by implementing the suggested method confirm that the solution approaches closer to the exact solution as the value tends from fractional order towards integer order. Moreover, the proposed method is interesting, easy, and highly accurate in solving various nonlinear fractional-order partial differential equations. The numerical results and their graphical simulations are presented using MATLAB.
  • [ X ]
    Öğe
    Approximate analytical solutions of the nonlinearfractional order financial model by two efficientmethods with a comparison study
    (Samara State Technical Univ, 2024) Liaqat, M. I.; Khan, A.; Irshad, A.; Akguel, A.; Prosviryakov, E.
    The financial system has become prominent and important in globaleconomics, because the key to stabilizing the economy is to secure or controlthe financial system or market. The goal of this study is to determine whether or not the approximateanalytical series solutions obtained by the residual power series method andElzaki transform decomposition method of the fractional nonlinear financialmodel satisfy economic theory. The fractional derivative is used in the senseof the Caputo derivative. The results are depicted numerically and in figures that show the behav-ior of the approximate solutions of the interest rate, investment demand,and price index. Both methods yielded results in accordance with economictheory, which established that researchers could apply these two methods tosolve various types of fractional nonlinear problems that arise in financialsystems