Application of the Extended F-Expansion Method for Solving the Fractional Gardner Equation With Conformable Fractional Derivative

In this study, we derive a new fractional Gardner equation with the conformable fractional derivative for the first time. Using the extended F-expansion method, different traveling wave solutions expressed in the form of the hyperbolic solutions such as sech, tanh, csch, coth, sinh and their combination, and the triangular solutions like csc, sec, tan, cot and their combination are obtained. Finally, the solutions are illustrated through the 3D plots. The results strongly prove that the proposed approach is effective and can help us understand the nonlinear problems arising in physics better.