Modeling economic growth dynamics: A fractional approach with 2D nonlinear Fisher equation

Abstract

This study presents a robust numerical investigation of the two-dimensional time-fractional Fisher equation (TFFE), incorporating both Caputo and conformable fractional derivatives, to model key dynamics of economic growth. By integrating a logistic growth term, the classical Fisher framework is extended to capture the non-local temporal memory and spatial diffusion effects characteristic of economic phenomena such as capital accumulation and technological diffusion. The spatial domain is discretized using a differential quadrature method (DQM) based on modified cubic trigonometric B-splines, effectively addressing the challenges posed by fractional operators. Temporal discretization yields fractional ordinary differential equations (FODEs), which are efficiently solved using a quasilinearization technique to handle nonlinearities. Numerical experiments demonstrate the method's accuracy and reliability, with stability confirmed via the Lax Richtmyer criterion. A comprehensive error analysis, convergence study, and sensitivity investigation further underscore the potential of the fractional framework to simulate complex, real-world economic behavior. The obtained results showcase the role of fractional and time parameters in perspectives through tables and figures.