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Browsing by Author "Tasbozan, O."

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    Citation - Scopus: 1
    Analytical and Numerical Solutions for Time-Fractional New Coupled Mkdv Equation Arising in Interaction of Two Long Waves
    (Asia Pacific Academic, 2019) Şenol, M.; Kurt, A.; Baleanu, D.; Tasbozan, O.; 56389; 06.04. Endüstri Mühendisliği; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 06. Mühendislik Fakültesi; 01. Çankaya Üniversitesi; 09. Rektörlük; 09.02. Yabancı Diller Bölümü
    The aim of this paper is to present new exact solution sets of nonlinear conformable time-fractional new coupled mKdV equations which arise in interaction of two long waves with different dispersion relations by means of sub-equation method. In addition, we also propose an analytical-approximate method namely residual power series method (RPSM) for the system. The fractional derivatives have been explained in newly defined conformable type, during the solution procedure. The exact solutions of the system obtained by the sub-equation method have been compared to approximate solutions derived by RPSM. The results showed that both methods are robust, dependable, easy to apply and a good alternative for seeking solutions of fractional partial differential equations. © 2019 Asia Pacific Journal of Mathematics.
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    Citation - WoS: 43
    Citation - Scopus: 50
    New Solutions for Conformable Fractional Nizhnik-Novikov System Via G'/g Expansion Method and Homotopy Analysis Methods
    (Springer, 2017) Tasbozan, O.; Baleanu, D.; Kurt, A.; 02.02. Matematik; 06.04. Endüstri Mühendisliği; 02. Fen-Edebiyat Fakültesi; 06. Mühendislik Fakültesi; 01. Çankaya Üniversitesi; 09. Rektörlük; 09.02. Yabancı Diller Bölümü
    The main purpose of this paper is to find the exact and approximate analytical solution of Nizhnik-Novikov-Veselov system which may be considered as a model for an incompressible fluid with newly defined conformable derivative by using G'/G expansion method and homotopy analysis method (HAM) respectively. Authors used conformable derivative because of its applicability and lucidity. It is known that, the NNV system of equations is an isotropic Lax integrable extension of the well-known KdV equation and has physical significance. Also, NNV system of equations can be derived from the inner parameter-dependent symmetry constraint of the KP equation. Then the exact solutions obtained by using G'/G expansion method are compared with the approximate analytical solutions attained by employing HAM.