Abstract
•Employing a generalized type of conformable fractional derivative to investigate some nonlinear evolution equations.•Introducing a modern technique for solving the Fractional nonlinear evolution equations.•Applying the above technique to find new exact solutions of the space-time fractional Schrodinger-Hirota equation and the space-time fractional modified KdV-Zakharov-Kuznetsov equation.•The results acquired confirm that the proposed GCFD is to describe the rigorous structure of complex physical phenomena without heredity and nonlocality.•The obtained solutions are compared with some past results from literature. Moreover, some of these solutions are physically interpreted and graphically sketched.
In this work, a generalized type of conformable local fractal derivative (GCFD) is employed to investigate some nonlinear evolution equations. A modern technique for solving the nonlinear evolution equations is introduced. This technique based on the GCFD, the first integral method, and the functional variable method. As applied examples, new exact solutions of the space-time local fractal Schrödinger-Hirota equation and the space-time local fractal modified KdV-Zakharov-Kuznetsov equation are established. The results acquired confirm that the proposed GCFD is to describe the rigorous structure of complex physical phenomena without heredity and nonlocality. The obtained solutions are compared with some past results from literature. Moreover, some of these solutions are physically interpreted and graphically sketched.