Yazar "Sakar, Mehmet Giyas" seçeneğine göre listele

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    A Novel Technique for Fractional Bagley-Torvik Equation
    (Natl Acad Sciences India, 2019) Sakar, Mehmet Giyas; Saldir, Onur; Akgul, Ali
    In this research, numerical solution of boundary value problem of fractional Bagley-Torvik equation is given in the reproducing kernel space. The central point of this approach is to set up a new reproducing kernel Hilbert space (RKHS) that satisfies the boundary conditions. Predicated on the properties of the RKHS, a new approach is applied to obtain precise numerical approximation. The results shows that a new approach is very effective and convenient for large interval.
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    Analytical Approximate Solutions of (n+1)-Dimensional Fractal Heat-Like and Wave-Like Equations
    (Mdpi, 2017) Acan, Omer; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Sakar, Mehmet Giyas
    In this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems.
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    Numerical Solution of Fractional Bratu Type Equations with Legendre Reproducing Kernel Method
    (Springer, 2018) Sakar, Mehmet Giyas; Saldır, Onur; Akgül, Ali
    In this research, a new numerical method is proposed for solving fractional Bratu type boundary value problems. Fractional derivatives are taken in Caputo sense. This method is predicated on iterative approach of reproducing kernel Hilbert space theory with shifted Legendre polynomials. Construction of iterative process is shown by orthogonal projection operator. Numerical results show that our method is effective and convenient for fractional Bratu type problem. © 2018, Springer Nature India Private Limited.
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    On solutions of fractional Riccati differential equations
    (Springer International Publishing Ag, 2017) Sakar, Mehmet Giyas; Akgul, Ali; Baleanu, Dumitru
    We apply an iterative reproducing kernel Hilbert space method to get the solutions of fractional Riccati differential equations. The analysis implemented in this work forms a crucial step in the process of development of fractional calculus. The fractional derivative is described in the Caputo sense. Outcomes are demonstrated graphically and in tabulated forms to see the power of the method. Numerical experiments are illustrated to prove the ability of the method. Numerical results are compared with some existing methods.