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Browsing by Author "Korpinar, Z."

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    Article
    Citation - Scopus: 12
    On the fractional model of fokker-planck equations with two different operator
    (American Institute of Mathematical Sciences, 2020) Korpinar, Z.; Inc, M.; Baleanu, D.; 56389; Matematik
    In this paper, the fractional model of Fokker-Planck equations are solved by using Laplace homotopy analysis method (LHAM). LHAM is expressed with a combining of Laplace transform and homotopy methods to obtain a new analytical series solutions of the fractional partial differential equations (FPDEs) in the Caputo-Fabrizio and Liouville-Caputo sense. Here obtained solutions are compared with exact solutions of these equations. The suitability of the method is removed from the plotted graphs. The obtained consequens explain that technique is a power and efficient process in investigation of solutions for fractional model of Fokker-Planck equations. © 2020 the Author(s), licensee AIMS Press.
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    Article
    Citation - Scopus: 7
    Some applications of the least squares-residual power series method for fractional generalized long wave equations
    (Shanghai Jiaotong University, 2021) Korpinar, Z.; Baleanu, D.; Inc, M.; Almohsen, B.; 56389; Matematik
    This article examines a new effective method called the least squares-residual power series method (LS-RPSM) and compares this method with the RPSM. The LS-RPSM assembles the least-squares process with the residual power series method. These techniques are applied to investigate the linear and nonlinear time-fractional regularized long wave equations (TFRLWEs). The RLW models define the shallow water waves in oceans and the internal ion-acoustic waves in plasma. Firstly, we apply the well-known RPSM to acquire approximate solutions. In the next step, the Wronskian determinant is searched in fractional order to show that the functions are linearly independent. After these operations, a system of linear equations is obtained. In the last step, the least-squares algorithm is used to find the necessary coefficients. When this article is examined, it can be said that LS-RPSM is more useful because it requires using fewer terms than the required number of terms when applying the RPSM. Additionally, the experiments show that this method converges better than RPSM. © 2021