Yücel Çenesiz

Bio: Yücel Çenesiz is an academic researcher from Selçuk University. The author has contributed to research in topics: Conformable matrix & Fractional calculus. The author has an hindex of 13, co-authored 18 publications receiving 675 citations.

New exact solutions of Burgers’ type equations with conformable derivative

Abstract: In this paper, the new exact solutions for some nonlinear partial differential equations are obtained within the newly established conformable derivative. We use the first integral method to establish the exact solutions for time-fractional Burgers’ equation, modified Burgers’ equation, and Burgers–Korteweg–de Vries equation. We report that this method is efficient and it can be successfully used to obtain new analytical solutions of nonlinear FDEs.

The solution of the Bagley–Torvik equation with the generalized Taylor collocation method

Abstract: In this paper, the Bagley–Torvik equation, which has an important role in fractional calculus, is solved by generalizing the Taylor collocation method. The proposed method has a new algorithm for solving fractional differential equations. This new method has many advantages over variety of numerical approximations for solving fractional differential equations. To assess the effectiveness and preciseness of the method, results are compared with other numerical approaches. Since the Bagley–Torvik equation represents a general form of the fractional problems, its solution can give many ideas about the solution of similar problems in fractional differential equations.

On the Solution of Burgers’ Equation with the New Fractional Derivative

Abstract: Abstract Firstly in this article, the exact solution of a time fractional Burgers’ equation, where the derivative is conformable fractional derivative, with dirichlet and initial conditions is found byHopf-Cole transform. Thereafter the approximate analytical solution of the time conformable fractional Burger’s equation is determined by using a Homotopy Analysis Method(HAM). This solution involves an auxiliary parameter ~ which we also determine. The numerical solution of Burgers’ equation with the analytical solution obtained by using the Hopf-Cole transform is compared.

New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method

Abstract: In this paper, the Jacobi elliptic function expansion method is proposed for the first time to construct the exact solutions of the time conformable fractional two-dimensional Boussinesq equation and the combined KdV-mKdV equation. New exact solutions are found. This method is based on Jacobi elliptic functions. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.

On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion

Abstract: 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.

New exact solutions of Burgers’ type equations with conformable derivative

Abstract: In this paper, the new exact solutions for some nonlinear partial differential equations are obtained within the newly established conformable derivative. We use the first integral method to establish the exact solutions for time-fractional Burgers’ equation, modified Burgers’ equation, and Burgers–Korteweg–de Vries equation. We report that this method is efficient and it can be successfully used to obtain new analytical solutions of nonlinear FDEs.

A generalization of truncated M-fractional derivative and applications to fractional differential equations

Abstract: In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]. To do that, we used generalized M-series, which has a more general form than Mittag-Leffler and hypergeometric functions. We called this generalization as truncated M-series fractional derivative. This new derivative generalizes several fractional derivatives and satisfies important properties of the integerorder derivatives. Finally, we obtain the analytical solutions of some M-series fractional differential equations.

New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method

Abstract: In this paper, the nonlinear Boussinesq equations with the conformable time-fractional derivative are solved analytically using the well-established modified Kudryashov method. As a consequence, a number of new exact solutions for this type of equations are formally derived. It is believed that the method is one of the most effective techniques for extracting new exact solutions of nonlinear fractional differential equations.