Accelerator and Multiplier for Macroeconomic Processes with Memory

Tarasova, Valentina V.

doi:10.21013/jmss.v9.v3.p1

Cited by 11 publications

(36 citation statements)

References 5 publications

(6 reference statements)

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“…where C(α) = A(α) · B(α). This form of the equation allows you to interpret the action of Caputo-Fabrizio fractional derivative, as a superposition (parallel action) of the standard accelerator and the multiplier without memory [11].…”

Section: Example 5: the Caputo-fabrizio Fractional Derivativementioning

confidence: 99%

“…This means that the nonlocal effects with respect cannot be described by this equation. Secondly, the nonlocality by time (dynamic memory) means a dependence of output (endogenous) variable at the present time on the changes of input (exogenous) variable on finite (or infinite) time interval of the past [10,11]. The memory can be considered as a property of processes, which characterizes the dependence of this process at a given time on the states in the past [10].…”

Section: Introductionmentioning

confidence: 99%

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No nonlocality. No fractional derivative

Tarasov

2018

Communications in Nonlinear Science and Numerical Simulation

Self Cite

177

104

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Abstract:The paper discusses the characteristic properties of fractional derivatives of non-integer order. It is known that derivatives of integer orders are determined by properties of differentiable functions only in an infinitely small neighborhood of the considered point. Therefore differential equation, which is considered for this point and contains a finite number of integer-order derivatives, cannot describe nonlocality in space and time. This allows us to propose a principle of nonlocality for fractional derivatives. We state that if the differential equation with fractional derivative can be presented as a differential equation with a finite number of integer-order derivatives, then this fractional derivative cannot be considered as a derivative of non-integer order. This means that all results obtained for this type of fractional derivatives can be derived by using differential operators with integer orders. To illustrate the application of the nonlocality principle, we prove that the conformable fractional derivative, the M-fractional derivative, the alternative fractional derivative, the local fractional derivative and the Caputo-Fabrizio fractional derivatives with exponential kernels cannot be considered as fractional derivatives of non-integer orders.

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Section: Example 5: the Caputo-fabrizio Fractional Derivativementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

No nonlocality. No fractional derivative

Tarasov

2018

Communications in Nonlinear Science and Numerical Simulation

Self Cite

177

104

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“…Let us briefly describe this generalized model with memory. The equation of investment accelerator with memory [37,39] can be written as…”

Section: Dynamic Keynesian Model With Memorymentioning

confidence: 99%

“…where Γ(α) is the gamma function and n − 1 < α ≤ n. Using 12, the accelerator with memory (10) is represented [37,39] as…”

Section: Dynamic Keynesian Model With Memorymentioning

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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Logistic equation with continuously distributed lag and application in economics

Tarasova

2019

Nonlinear Dyn

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Accelerator and Multiplier for Macroeconomic Processes with Memory

Abstract: ABSTRACT

Cited by 11 publications

References 5 publications

No nonlocality. No fractional derivative

No nonlocality. No fractional derivative

Dynamic Keynesian Model of Economic Growth with Memory and Lag

Logistic equation with continuously distributed lag and application in economics

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