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Öğe An approach to time fractional gas dynamics equation: Quadratic B-spline Galerkin method(Elsevier Science Inc, 2015) Esen, A.; Tasbozan, O.In the present article, a quadratic B-spline finite element Galerkin method has been used to obtain numerical solutions of the nonlinear time fractional gas dynamics equation. While the Caputo form is used for the time fractional derivative appearing in the equation, the L1 discretization formula is applied to the equation in time. A numerical example is given and the obtained results show the accuracy and efficiency of the method. Therefore, the present method can be used as an efficient alternative one to find out the numerical solutions of other both linear and nonlinear fractional differential equations available in the literature. (C) 2015 Elsevier Inc. All rights reserved.Öğe Cubic B-spline collocation method for solving time fractional gas dynamics equation(De Gruyter Open Ltd, 2015) Esen, A.; Tasbozan, O.To the present manuscript, a cubic B-spline finite element collocation method has been used to obtain numerical solutions of the nonlinear time fractional gas dynamics equation. While the Caputo form is used for the time fractional derivative appearing in the equation, the L1 discretization formula is applied to the equation in terms of time. It has been seen that the results of the present study are in agreement with the those of exact solution. Therefore, the present method can be used as an alternative and efficient one to find out the numerical solutions of both linear and nonlinear fractional differential equations available in the literature. In order to control the accuracy and efficiency of the present method, the error norms L-2, and L-infinity have been calculated. It is evident that, the newly obtained numerical solutions by the present method can he computed easily with the implementation and effectiveness of the approach used in the article.Öğe New solutions for conformable fractional Nizhnik-Novikov-Veselov system via G'/G expansion method and homotopy analysis methods(Springer, 2017) Kurt, A.; Tasbozan, O.; Baleanu, D.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.Öğe Numerical solution of time fractional Burgers equation(De Gruyter Poland Sp Zoo, 2015) Esen, A.; Tasbozan, O.In this article, the time fractional order Burgers equation has been solved by quadratic B-spline Galerkin method. This method has been applied to three model problems. The obtained numerical solutions and error norms L-2 and L-infinity have been presented in tables. Absolute error graphics as well as those of exact and numerical solutions have been given.Öğe On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion(Pergamon-Elsevier Science Ltd, 2017) Iyiola, O. S.; Tasbozan, O.; Kurt, A.; Cenesiz, Y.In this paper, we consider the system of conformable time-fractional Robertson equations with one-dimensional diffusion having widely varying diffusion coefficients. Due to the mismatched nature of the initial and boundary conditions associated with Robertson equation, there are spurious oscillations appearing in many computational algorithms. Our goal is to obtain an approximate solutions of this system of equations using the q-homotopy analysis method (q-HAM) and examine the widely varying diffusion coefficients and the fractional order of the derivative. Published by Elsevier Ltd.
