Eur. Phys. J. Special Topics 226, 3811–3825 (2017)
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

Abstract

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.