scholarly journals Dynamic Keynesian Model of Economic Growth with Memory and Lag

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 178 ◽  
Author(s):  
Vasily Tarasov ◽  
Valentina Tarasova
Keyword(s):  
Differential Equation ◽  
Economic Growth ◽  
Fractional Differential Equation ◽  
Differential Operators ◽  
Continuous Distribution ◽  
National Income ◽  
Fading Memory ◽  
Kummer Functions ◽  
Distributed Lag ◽  
Fractional Differential

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.

scholarly journals Harrod–Domar Growth Model with Memory and Distributed Lag

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 9 ◽  
Author(s):  
Vasily E. Tarasov ◽  
Valentina V. Tarasova
Keyword(s):  
Asymptotic Behavior ◽  
Time Delay ◽  
Growth Model ◽  
National Income ◽  
Fading Memory ◽  
Distributed Lag ◽  
Distributed Time Delay ◽  
Fractional Differential ◽  
With Memory ◽  
Macroeconomic Growth

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.

scholarly journals Application of fractional differential equation in economic growth model: A systematic review approach

2021 ◽  
Vol 6 (9) ◽  
pp. 10266-10280
Author(s):  
Muhamad Deni Johansyah ◽  
◽  
Asep K. Supriatna ◽  
Endang Rusyaman ◽  
Jumadil Saputra ◽  
...  
Keyword(s):  
Differential Equation ◽  
Economic Growth ◽  
Systematic Review ◽  
Fractional Differential Equation ◽  
Growth Model ◽  
Economic Growth Model ◽  
Fractional Differential

scholarly journals Fractional Differential Equation-Based Instantaneous Frequency Estimation for Signal Reconstruction

2021 ◽  
Vol 5 (3) ◽  
pp. 83
Author(s):  
Bilgi Görkem Yazgaç ◽  
Mürvet Kırcı
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Frequency Estimation ◽  
Signal Reconstruction ◽  
Reconstruction Method ◽  
Reconstruction Algorithms ◽  
Instantaneous Frequency Estimation ◽  
Proposed Model ◽  
Fractional Differential ◽  
Instantaneous Frequencies

In this paper, we propose a fractional differential equation (FDE)-based approach for the estimation of instantaneous frequencies for windowed signals as a part of signal reconstruction. This approach is based on modeling bandpass filter results around the peaks of a windowed signal as fractional differential equations and linking differ-integrator parameters, thereby determining the long-range dependence on estimated instantaneous frequencies. We investigated the performance of the proposed approach with two evaluation measures and compared it to a benchmark noniterative signal reconstruction method (SPSI). The comparison was provided with different overlap parameters to investigate the performance of the proposed model concerning resolution. An additional comparison was provided by applying the proposed method and benchmark method outputs to iterative signal reconstruction algorithms. The proposed FDE method received better evaluation results in high resolution for the noniterative case and comparable results with SPSI with an increasing iteration number of iterative methods, regardless of the overlap parameter.

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

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