Yazar "Wannan, Rania" seçeneğine göre listele

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    Fractional Order Techniques for Stiff Differential Equations Arising from Chemistry Kinetics
    (New York Business Global Llc, 2022) Wannan, Rania; Aslam, Muhammad; Farman, Muhammad; Akgul, Ali; Kouser, Farhina; Asad, Jihad
    In this paper, we consider the stiff systems of ordinary differential equations arising from chemistry kinetics. We develop the fractional order model for chemistry kinetics problems by using the Caputo Fabrizio and Atangana-Baleanu derivatives in Caputo sense. We apply the Sumudu transform to obtain the solutions of the models. Uniqueness and stability analysis of the problem are also established by using the fixed point theory results. Numerical results are obtained by using the proposed schemes which supports theoretical results. These concepts are very important for using the real-life problems like Brine tank cascade, Recycled Brine tank cascade, pond pollution, home heating and biomass transfer problem. These results are crucial for solving the nonlinear model in chemistry kinetics.
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    Kernel Functions and New Applications of an Accurate Technique
    (Natural Sciences Publishing, 2023) Wannan, Rania; Akg, Ali; Akg, Esra Karatas; Hasan, Eyad Hasan; Asad, Jihad
    In this article, some general reproducing kernel Sobolev spaces was constructed. We find the general functions in these reproducing kernel Sobolev spaces. Many higher order boundary value problems can be investigated by these special functions. © 2023 NSP.
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    Novel Exact and Solitary Wave Solutions for The Time-Fractional Nonlinear Maccari's System
    (Universal Wiser Publisher, 2023) Gasmi, Boubekeur; Alhakim, Lama; Mati, Yazid; Moussa, Alaaeddin; Akgul, Ali; Wannan, Rania; Asad, Jihad
    The purpose of this research is to find analytical solutions to the time-fractional nonlinear Maccari system. The double auxiliary equation method, which has never been used before, is used to obtain these solutions. The method is cleverly applied, resulting in the generation of nine new exact solitary wave solutions that have never been found before. We also describe the system's dynamic behavior and the bifurcation of traveling waves. Finally, we show some solutions with different coefficient values that correspond to the nine discovered solutions graphically.
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    Solving the time-fractional inverse Burger equation involving fractional Heydari-Hosseininia derivative
    (Amer Inst Mathematical Sciences-Aims, 2022) Partohaghighi, Mohammad; Akgul, Ali; Asad, Jihad; Wannan, Rania
    Heydari-Hosseininia (HH) fractional derivative is a newly introduced concept of fractional calculus which conquers the restrictions of non-singular fractional derivatives in the Caputo-Fabrizio (CF) and Atangana-Baleanu senses. For instance, it is not easy to get the closed-form of the fractional derivative of functions using CF because of the construction of its kernel function. In this paper, we present a powerful numerical scheme based on energy boundary functions to get the approximate solutions of the time-fractional inverse Burger equation containing HH-derivative: (HH)D(tau)(alpha)h(z, tau) - h(z, tau)h(z)(z, tau) = h(zz)(z, tau) + H(z, tau), which (HH)D(alpha)(tau )is the HH-derivative with regard to alpha-order. This problem has never been investigated earlier so, this is our motivation to work on this important problem. Some numerical examples are presented to verify the efficiency of the presented technique. Graphs of the exact and numerical solutions along with the plot of absolute error are provided for each example. Tables are given to see and compare the results point by point for each example.