On the boundedness of nonoscillatory solutions of certain fractional differential equations with positive and negative terms

This paper deals with the boundedness of nonoscillatory solutions of the forced fractional differential equation with positive and negative terms (C)D(c)(alpha)y(t) + f(t,x(t)) = e(t) + k(t)x(t) + h(t, x(t)), where t >= c, alpha is an element of (0, 1), c > 1, and (C)D(c)(alpha)y denotes the Caputo fractional derivative of y of order alpha. The cases where y(t) = (a(t)x'(t))' and y(t) = a(t)x'(t). are considered. The technique used can be applied to other related fractional differential equations. Examples are inserted to illustrate the relevance of the results obtained. (C) 2019 Elsevier Ltd. All rights reserved.