https://doi.org/10.1140/epjst/e2018-00033-9
Regular Article
A fractional-order impulsive delay model of price fluctuations in commodity markets: almost periodic solutions
1
Department of Mathematics, University of Santiago de Compostela,
15782
Santiago de Compostela, Spain
2
Department of Mathematics, Faculty of Science, King Abdulaziz University,
P.O. Box 80203,
Jeddah
21589, Saudi Arabia
3
Technical University, Department of Mathematics and Physics,
Sliven
8800, Bulgaria
4
University of Texas at San Antonio, Department of Mathematics,
San Antonio,
TX
78249, USA
a e-mail: gstamov@abv.bg
Received:
17
June
2017
Received in final form:
23
August
2017
Published online: 25
July
2018
In this paper an impulsive time-varying model for the dynamics of price adjustment in a single commodity market using the Caputo fractional-order derivative is developed. Applying the fractional Lyapunov method and Mittag-Leffler functions, we give sufficient conditions for the existence of an almost periodic solution. The uniform asymptotic stability and Mittag-Leffler stability are also considered.
© EDP Sciences, Springer-Verlag 2018