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

Document Type : Research Article

Authors

D. L. Suthar ¹

Fasil Desalew ¹

Mulualem Aychluh ²

Gizachew Tirite ³

¹ Department of Mathematics, Wollo University, Dessie, Ethiopia.

² Department of Mathematics, Samara University, Samara, Ethiopia.

³ Department of Mathematics, Debre Tabor University, Debre Tabor, Ethiopia.

10.22067/ijnao.2026.96531.1779

Abstract

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.

Keywords

Fisher-KPP equation

Power series method

Conformable fractional derivative

Subjects

• Numerical methods for differential equations and its applications

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