Yazar "Ozdemir, Necati" seçeneğine göre listele

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    COMPARING THE NEW FRACTIONAL DERIVATIVE OPERATORS INVOLVING EXPONENTIAL AND MITTAG-LEFFLER KERNEL
    (Amer Inst Mathematical Sciences-Aims, 2020) Yavuz, Mehmet; Ozdemir, Necati
    In this manuscript, we have proposed a comparison based on newly defined fractional derivative operators which are called as Caputo-Fabrizio (CF) and Atangana-Baleanu (AB). In 2015, Caputo and Fabrizio established a new fractional operator by using exponential kernel. After one year, Atangana and Baleanu recommended a different-type fractional operator that uses the generalized Mittag-Leffler function (MLF). Many real-life problems can be modelled and can be solved by numerical-analytical solution methods which are derived with these operators. In this paper, we suggest an approximate solution method for PDEs of fractional order by using the mentioned operators. We consider the Laplace homotopy transformation method (LHTM) which is the combination of standard homotopy technique (SHT) and Laplace transformation method (LTM). In this study, we aim to demonstrate the effectiveness of the aforementioned method by comparing the solutions we have achieved with the exact solutions. Furthermore, by constructing the error analysis, we test the practicability and usefulness of the method.
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    European Vanilla Option Pricing Model of Fractional Order without Singular Kernel
    (Mdpi, 2018) Yavuz, Mehmet; Ozdemir, Necati
    Recently, fractional differential equations (FDEs) have attracted much more attention in modeling real-life problems. Since most FDEs do not have exact solutions, numerical solution methods are used commonly. Therefore, in this study, we have demonstrated a novel approximate-analytical solution method, which is called the Laplace homotopy analysis method (LHAM) using the Caputo-Fabrizio (CF) fractional derivative operator. The recommended method is obtained by combining Laplace transform (LT) and the homotopy analysis method (HAM). We have used the fractional operator suggested by Caputo and Fabrizio in 2015 based on the exponential kernel. We have considered the LHAM with this derivative in order to obtain the solutions of the fractional Black-Scholes equations (FBSEs) with the initial conditions. In addition to this, the convergence and stability analysis of the model have been constructed. According to the results of this study, it can be concluded that the LHAM in the sense of the CF fractional derivative is an effective and accurate method, which is computable in the series easily in a short time.
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    New Numerical Techniques for Solving Fractional Partial Differential Equations in Conformable Sense
    (Springer, 2019) Yavuz, Mehmet; Ozdemir, Necati
    This study adresses two new numerical techniques for solving some interesting one-dimensional time-fractional partial differential equations (PDEs). We have introduced modified homotopy perturbation method in conformable sense (MHPMC) and Adomian decomposition method in conformable sense (ADMC) which improve the solutions for linear-nonlinear fractional PDEs. In order to show the efficiencies of these methods, we have compared the numerical and exact solutions of three illustrative problems. Also, we have declared that the proposed models are very efficient and powerful techniques in finding approximate-analytical solutions for the PDEs of fractional order in conformable sense.
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    On the Solutions of Fractional Cauchy Problem Featuring Conformable Derivative
    (E D P Sciences, 2018) Yavuz, Mehmet; Ozdemir, Necati
    In this study, we have obtained analytical solutions of fractional Cauchy problem by using q-Homotopy Analysis Method (q-HAM) featuring conformable derivative. We have considered different situations according to the homogeneity and linearity of the fractional Cauchy differential equation. A detailed analysis of the results obtained in the study has been reported. According to the results, we have found out that our obtained solutions approach very speedily to the exact solutions.
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    Real data-based optimal control strategies for assessing the impact of the Omicron variant on heart attacks
    (Amer Inst Mathematical Sciences-Aims, 2023) Evirgen, Firat; Ozkose, Fatma; Yavuz, Mehmet; Ozdemir, Necati
    This paper presents an investigation into the relationship between heart attacks and the Omicron variant, employing a novel mathematical model. The model incorporates two adjustable control parameters to manage the number of infected individuals and individuals with the Omicron variant. The study examines the model's positivity and boundedness, evaluates the reproduction number (R0), and conducts a sensitivity analysis of the control parameters based on the reproduction number. The model's parameters are estimated using the widely utilized least squares curve fitting method, employing real COVID-19 cases from Tu & BULL;rkiye. Finally, numerical simulations demonstrate the efficacy of the suggested controls in reducing the number of infected individuals and the Omicron population.
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    Solutions of partial differential equations using the fractional operator involving Mittag-Leffler kernel
    (Springer Heidelberg, 2018) Yavuz, Mehmet; Ozdemir, Necati; Baskonus, Haci Mehmet
    In this paper, time-fractional partial differential equations (FPDEs) involving singular and nonsingular kernel are considered. We have obtained the approximate analytical solution for linear and nonlinear FPDEs using the Laplace perturbation method (LPM) defined with the Liouville-Caputo (LC) and Atangana-Baleanu (AB) fractional operators. The AB fractional derivative is defined with the Mittag-Leffler function and has all the properties of a classical fractional derivative. In addition, the AB operator is crucial when utilizing the Laplace transform (LT) to get solutions of some illustrative problems with initial condition. We show that the mentioned method is a rather effective and powerful technique for solving FPDEs. Besides, we show the solution graphs for different values of fractional order a, distance term x and time value t. The classical integer-order features are fully recovered if a is equal to 1.