TY  - JOUR
ID  - Graef2020
LB  - Graef2020
AU  - Graef, John R.
AU  - Grace, Said R.
AU  - Tunç, Ercan
TI  - On the asymptotic behavior of nonoscillatory solutions of certain fractional differential equations with positive and negative terms
ST  - On the asymptotic behavior of nonoscillatory solutions of certain fractional differential equations with positive and negative terms
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 2
SP  - 227
EP  - 239
DO  - https://doi.org/10.7494/OpMath.2020.40.2.227
UR  - https://doi.org/10.7494/OpMath.2020.40.2.227
AB  - This paper is concerned with the asymptotic behavior of the nonoscillatory solutions of the forced fractional differential equation with positive and negative terms of the form \[^{C}D_{c}^{\alpha}y(t)+f(t,x(t))=e(t)+k(t)x^{\eta}(t)+h(t,x(t)),\] where \(t\geq c \geq 1\), \(\alpha \in (0,1)\), \(\eta \geq 1\) is the ratio of positive odd integers, and \(^{C}D_{c}^{\alpha}y\) denotes the Caputo fractional derivative of \(y\) of order \(\alpha\). The cases \[y(t)=(a(t)(x^{\prime}(t))^{\eta})^{\prime} \quad \text{and} \quad y(t)=a(t)(x^{\prime}(t))^{\eta}\] are considered. The approach taken here can be applied to other related fractional differential equations. Examples are provided to illustrate the relevance of the results obtained.
KW  - integro-differential equations
KW  - fractional differential equations
KW  - nonoscillatory solutions
KW  - boundedness
KW  - Caputo derivative
SN  - 1232-9274
ER  -