Browsing by Author "Guvenilir, A. Feza"

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Citation - WoS: 4
Citation - Scopus: 5
Nabla Discrete Fractional Gruss Type Inequality
(Springeropen, 2014) Peterson, Allan C.; Tas, Kenan; Guvenilir, A. Feza; Kaymakcalan, Billur
Properties of the discrete fractional calculus in the sense of a backward difference are introduced and developed. Here, we prove a more general version of the Gruss type inequality for the nabla fractional case. An example of our main result is given.
Citation - WoS: 4
Citation - Scopus: 5
Necessary and Sufficient Condition for Existence of Periodic Solutions of Predator-Prey Dynamic Systems With Beddington-Deangelis Functional Response
(Springeropen, 2016) Guvenilir, A. Feza; Kaymakcalan, Billur; Pelen, Neslihan Nesliye
We consider two-dimensional predator-prey systems with Beddington-DeAngelis-type functional response on periodic time scales. For this special case, we try to find the necessary and sufficient conditions for the considered system when it has at least one w-periodic solution. This study is mainly based on continuation theorem in coincidence degree theory and will also give beneficial results for continuous and discrete cases. Especially, for the continuous case, by using the study of Cui and Takeuchi (J. Math. Anal. Appl. 317: 464-474, 2006), to obtain the globally attractive w-periodic solution of the given system, an inequality is given as a necessary and sufficient condition. Additionally, for the continuous case in this study, the open problem given in the discussion part of the study of Fan and Kuang (J. Math. Anal. Appl. 295: 15-39, 2004) is solved.