Abstract
In this paper, we propose a macroeconomic growth model, in which we take into account memory with power-law fading and gamma distributed lag. This model is a generalization of the standard Harrod–Domar growth model. Fractional differential equations of this generalized model with memory and lag are suggested. For these equations, we obtain solutions, which describe the macroeconomic growth of national income with fading memory and distributed time-delay. The asymptotic behavior of these solutions is described.
Highlights
Fractional differential equations are equations that contain derivatives of non-integer orders.There are many different types of such operators, among which the most famous are the fractional derivatives that are proposed by Liouville and Riemann, Letnikov and Grünwald, Riesz, Hadamard, Erdelyi and Kober, Caputo [1,2,3,4,5,6]
We propose a generalization of the Harrod–Domar growth model [8,9,10,11,12], in which the dynamics of national income is described by fractional differential equations with continuously distributed time delay
The Harrod–Domar growth model with power-law memory was suggested by authors in References [15,16,17,18]
Summary
Fractional differential equations are equations that contain derivatives of non-integer orders. We propose a generalization of the Harrod–Domar growth model [8,9,10,11,12], in which the dynamics of national income is described by fractional differential equations with continuously distributed time delay. The Harrod–Domar growth model with power-law memory was suggested by authors [15,16]. In this paper, we consider one-parameter power-law memory and gamma distributed time delay. We propose the fractional differential equations of generalization of the Harrod–Domar growth model. Axioms 2019, 8, 9 describe the macroeconomic growth of national income with power-law fading memory and gamma distributed time-delay. The asymptotic behavior of the solutions, which characterize the technological growth rate of national income for the case of the Erlang distribution of delay time, is suggested
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