Applying Fractional Calculus to Analyze Economic Growth Modelling

Luo, Dahui; Wang, J. R.; Fečkan, Michal

doi:10.2478/jamsi-2018-0003

Cited by 27 publications

(20 citation statements)

References 20 publications

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“…The distributed lag leads to slower growth. We assume that the suggested approach and model can be used for economic growth modeling by analogy with the computer simulation of the economy in [54][55][56][57][58]. It should also be noted that fractional differential Equations have been applied to describe power-law memory in continuous-time finance [59][60][61][62][63][64][65][66][67][68][69][70][71][72].…”

Section: Discussionmentioning

confidence: 99%

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Dynamic Keynesian Model of Economic Growth with Memory and Lag

Tarasova

2019

Mathematics

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A mathematical model of economic growth with fading memory and continuous distribution of delay time is suggested. This model can be considered as a generalization of the standard Keynesian macroeconomic model. To take into account the memory and gamma-distributed lag we use the Abel-type integral and integro-differential operators with the confluent hypergeometric Kummer function in the kernel. These operators allow us to propose an economic accelerator, in which the memory and lag are taken into account. The fractional differential equation, which describes the dynamics of national income in this generalized model, is suggested. The solution of this fractional differential equation is obtained in the form of series of the confluent hypergeometric Kummer functions. The asymptotic behavior of national income, which is described by this solution, is considered.

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Section: Discussionmentioning

confidence: 99%

“…[ω λ −a , λ t] is defined by Equation (57). The second step is to find a particular solution (54) of Equation (55).…”

Section: Theorem 1 the Fractional Differential Equationmentioning

confidence: 99%

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Dynamic Keynesian Model of Economic Growth with Memory and Lag

Tarasova

2019

Mathematics

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“…We assume that this model can be used to economic growth modeling by using a generalization of methods applied in References [49][50][51][52][53][54][55].…”

Section: Discussionmentioning

confidence: 99%

Harrod–Domar Growth Model with Memory and Distributed Lag

Tarasova

2019

Axioms

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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.

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“…(5) Rituparna Pakhira, Uttam Ghosh and Susmita Sarkar derived [209][210][211][212][213] some inventory models with memory. (6) Computer simulation for modeling the national economies in the framework of the fractional generalizations of the Gross domestic product (GDP) model was proposed by Inés Tejado, Duarte Valério, Nuno Valério, Pedro Pires [214][215][216][217][218][219][220] in 2014-2019, and by Dahui Luo, JinRong Wang, Michal Feckan in 2018 in the paper [221]. 7In addition, we may note the works with economic models that were proposed in [100][101][102][103][104][105] that are related to the deterministic chaos stage.…”

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confidence: 99%

On History of Mathematical Economics: Application of Fractional Calculus

Tarasov

2019

Mathematics

173

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Modern economics was born in the Marginal revolution and the Keynesian revolution. These revolutions led to the emergence of fundamental concepts and methods in economic theory, which allow the use of differential and integral calculus to describe economic phenomena, effects, and processes. At the present moment the new revolution, which can be called “Memory revolution”, is actually taking place in modern economics. This revolution is intended to “cure amnesia” of modern economic theory, which is caused by the use of differential and integral operators of integer orders. In economics, the description of economic processes should take into account that the behavior of economic agents may depend on the history of previous changes in economy. The main mathematical tool designed to “cure amnesia” in economics is fractional calculus that is a theory of integrals, derivatives, sums, and differences of non-integer orders. This paper contains a brief review of the history of applications of fractional calculus in modern mathematical economics and economic theory. The first stage of the Memory Revolution in economics is associated with the works published in 1966 and 1980 by Clive W. J. Granger, who received the Nobel Memorial Prize in Economic Sciences in 2003. We divide the history of the application of fractional calculus in economics into the following five stages of development (approaches): ARFIMA; fractional Brownian motion; econophysics; deterministic chaos; mathematical economics. The modern stage (mathematical economics) of the Memory revolution is intended to include in the modern economic theory new economic concepts and notions that allow us to take into account the presence of memory in economic processes. The current stage actually absorbs the Granger approach based on ARFIMA models that used only the Granger–Joyeux–Hosking fractional differencing and integrating, which really are the well-known Grunwald–Letnikov fractional differences. The modern stage can also absorb other approaches by formulation of new economic notions, concepts, effects, phenomena, and principles. Some comments on possible future directions for development of the fractional mathematical economics are proposed.

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Applying Fractional Calculus to Analyze Economic Growth Modelling

Cited by 27 publications

References 20 publications

Dynamic Keynesian Model of Economic Growth with Memory and Lag

Dynamic Keynesian Model of Economic Growth with Memory and Lag

Harrod–Domar Growth Model with Memory and Distributed Lag

On History of Mathematical Economics: Application of Fractional Calculus

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