Fractional Dynamics of Natural Growth and Memory Effect in Economics

Abstract

A generalization of the economic model of natural growth, which takes into account the power-law memory effect, is suggested. The memory effect means the dependence of the process not only on the current state of the process, but also on the history of changes of this process in the past. For the mathematical description of the economic process with power-law memory we used the theory of derivatives of non-integer order and fractional-order differential equation. We propose equations take into account the effects of memory with one-parameter power-law damping. Solutions of these fractional differential equations are suggested. We proved that the growth and downturn of output depend on the memory effects. We demonstrate that the memory effect can lead to decrease of output instead of its growth, which is described by model without memory effect. Memory effect can lead to increase of output, rather than decrease, which is described by model without memory effect.

arXiv comment11 pages, PDF

References in corpus (6)

• Fractional calculus and continuous-time finance
• Fractional calculus and continuous-time finance II: the waiting-time distribution
• Logistic map with memory from economic model
• Economic interpretation of fractional derivatives
• Long and Short Memory in Economics: Fractional-Order Difference and Differentiation
• Economic Accelerator with Memory: Discrete Time Approach

Cited by in corpus (6)

• Concept of dynamic memory in economics
• Analysis of dispersion and propagation properties in a periodic rod using a space-fractional wave equation
• Dynamic intersectoral models with power-law memory
• Economic Growth Model with Constant Pace and Dynamic Memory
• Accelerators in macroeconomics: Comparison of discrete and continuous approaches
• Dynamic Model for Network Selection in Next Generation HetNets with Memory-affecting Rational Users