Analytical methods for non-linear fractional Kolmogorov-Petrovskii-Piskunov equation: Soliton solution and operator solution

Kolmogorov-Petrovskii-Piskunov equation can be regarded as a generalized form of the Fitzhugh-Nagumo, Fisher and Huxley equations which have many applications in physics, chemistry biology. In this paper, two fractional ex-tended versions non-linear are solved by analytical methods. Firstly, new more general derivative is defined some properties it given. Secondly, solution operator representation with obtained. Finally, exact solutions including kink-soliton other Khalil et al.?s variable coefficients It shown that fractional-order affects propagation velocity obtained solution.