A class of economic growth model with memory in the context of fractional derivatives

Tóm tắt

This article presents a model of economic growth that considers the effects of generalized power-law fading memory. To consider the memory effects in macroeconomic models, we propose a class of fractional differential equations involving a Caputo-type fractional derivative with respect to another function (or -Caputo derivative). For this purpose, the objective of this paper is to obtain the unique solution of the proposed -Caputo fractional differential equation. Behaviors of Mittag-Leffler’s functions, which characterize the growth behaviors of the solution are described. To evaluate the solution, we will compute the Mittag-Leffler functions by Matlab code. As a result, we obtain the solutions in explicit form. This work also provides a comparative analysis of solutions of our model and model without memory effect. To the best of our knowledge, the Harrod-Domar fractional differential equation with Caputo-type fractional derivative has not yet been investigated. Hence the result obtained from our study is essentially new. Moreover, this approach allows for greater flexibility in modeling economic behavior, making it possible to account for non-instantaneous effects and the cumulative impact of previous decisions.