Eur. Phys. J. Special Topics 226, 3657–3665 (2017)
https://doi.org/10.1140/epjst/e2018-00043-1

Regular Article

On the asymptotic behavior of nonoscillatory solutions of certain fractional differential equations

¹ Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Orman, Giza 12221, Egypt
² Department of Mathematics, Faculty of Engineering and Technology, American University of the Middle East, Kuwait

^a e-mail: agacik.zafer@aum.edu.kw

Received: 11 July 2017
Received in final form: 23 August 2017
Published online: 5 July 2018

Abstract

This paper deals with the asymptotic behavior of nonoscillatory solutions of fractional differential equations of the form

   _CD_a^αy = e(t) + f(t,x),  t ≥ a

where 0 < α < 1, a ≥ 0, _CD_a^αy denotes the Caputo fractional derivative of order α of y. The following particular cases are considered:

   y = (r(t)|x′|^δ-1x′)′,  (δ ≥ 1),   y = x′,  y = x.

We offer a method that can be applied to investigate more general class of fractional differential equations as well.