SOLVING TIME-FRACTIONAL FISHER MODELS BY NON-POLYNOMIAL SPLINES IN TERMS OF LOGARITHMIC DERIVATIVES

This paper introduces a novel numerical approach, the logarithmic non-polynomial spline method (LNPSM), leveraging a non-polynomial spline function with logarithmic terms to solve the conformable time-fractional Fisher (TFF) equation. The developed scheme achieves six-order convergence, derived through truncation error analysis and the Taylor series expansion. Stability is ensured under conditional constraints verified by von Neumann stability analysis. The method’s accuracy is demonstrated through two test examples, with results presented in comparison tables alongside cubic B-spline and Caputo non-polynomial spline methods, evaluated by norm errors. Additionally, graphical representations, including 2D and 3D plots, further illustrate the effectiveness of LNPSM. The findings indicate that LNPSM is a suitable and robust tool for solving time-fractional differential equations.