Yazar "Akgül, Esra Karatas" seçeneğine göre listele

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    A Novel Method for Solving Nonlinear Jerk Equations
    (Springer Science and Business Media Deutschland GmbH, 2021) Akgül, Ali; Akgül, Esra Karatas
    In this article, reproducing kernel method for solving Jerk equations is given. Convergence of the solution is shown. This method is applied to the equation for chosen values of the parameters that seem in the model and some numerical experiments prove that the reproducing kernel method is very effective method. © 2020, Springer Nature Switzerland AG.
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    Analysis of e-cigarette smoking model by a novel technique
    (Elsevier, 2022) Akgül, Ali; Akgül, Esra Karatas
    In this chapter, we research an e-cigarette smoking model with the fractal-fractional derivatives. We use three different (power-law, exponential-decay, and Mittag-Leffler) kernels in the model. We apply a novel technique to the model. We obtain the numerical simulations to show the accuracy of the proposed method. © 2022 Elsevier Inc. All rights reserved.
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    Analysis of the Fractal-Fractional Modelling of Immune-Tumor Problem
    (Springer, 2022) Partohaghighi, Mohammad; Rubasinghe, Kalani; Akgül, Ali; Akgül, Esra Karatas
    Cancer is one of the biggest threats around the globe, albeit medical action has been prosperous, despite large challenges, at least for some diagnostics. A magnificent effort of personal and financial resources is dedicated, with flourishing results(but also with failures), to cancer analysis with special consideration to experimental and analytical immunology. Fractal-fractional operators have manifested the enigmatic performance of numerous natural phenoms, which ordinarily do not foretell in ordinary ones and fractional operators. In this study, we examine an Immune-Tumor dynamical system supporting the fractal-fractional frame. We authenticate the existence theory to guarantee the suggested system maintains at least one answer through Schauder’s fixed point theorem. Additionally, Banach’s fixed theory affirms the uniqueness of the answer to the aimed problem. A Non-linear functional examination was carried out to affirm that the introduced system is stable with respect to Ulam-Hyres’s theory supporting the fractal-fractional operator. Behavior of the offered problem is presented through the graphical representations, for the different amounts of fractional order and fractal orders successfully. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.
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    On solutions of the kinetic model by sumudu transform
    (Bentham Science Publishers, 2023) Akgül, Esra Karatas; Belgacem, Fethi Bin Muhammed; Akgül, Ali
    This paper investigates the kinetic model with four different fractional derivatives. We obtain the solutions of the models by Sumudu transform and demonstrate our results with some figures. We prove the accuracy of the Sumudu transform by some theoretical results and applications. ©2023 Bentham Science Publishers.
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    Solving a New Type of Fractional Differential Equation by Reproducing Kernel Method
    (Springer Science and Business Media Deutschland GmbH, 2021) Akgül, Ali; Akgül, Esra Karatas
    The aim of this work is to get the solutions of the fractional counterpart of a boundary value problem by implementing the reproducing kernel Hilbert space method. Convergence of the solution problem discussed has been shown. The efficiency of the proposed technique is demonstrated by some tables. © 2020, Springer Nature Switzerland AG.