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    New Fractional Complex Transform for Conformable Fractional Partial Differential Equations
    (De Gruyter Open Ltd, 2016) Cenesiz, Y.; Kurt, A.
    Conformable fractional complex transform is introduced in this paper for converting fractional partial differential equations to ordinary differential equations. Hence analytical methods in advanced calculus can be used to solve these equations. Conformable fractional complex transform is implemented to fractional partial differential equations such as space fractional advection diffusion equation and space fractional telegraph equation to obtain the exact solutions of these equations.
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    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.
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    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.