Conformable fractional power series method for solving Fisher-Kolmogorov-Petrovskii-Piskunov equation

This work discusses the application of the conformable fractional power series method to approximate the nonlinear time-fractional Fisher–Kolmogorov–Petrovskii–Piskunov equation, which is used to model tumour growth and invasion. By employing the conformable derivative, the method converts the fractional equation into a recursive series expansion, resulting in accurate semi-analytical approximations. Three numerical examples involving various nonlinear powers have been solved. Analyses of convergence and error for the series solution have been conducted. The results show a remarkable agreement with both the exact solutions and existing numerical results, with very small absolute errors observed in all test cases. The results show a remarkable agreement with both the exact solutions and existing numerical results, with very small absolute errors observed in all test examples.

کلیدواژه ها:

Fisher-KPP equation ، Power series method ، Conformable fractional derivative