eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2019-09-12 7 5 124 134 10.12691/tjant-7-5-1 TJANT2019751 article Ugur Duran mtdrnugur@gmail.com, ugur.duran@iste.edu.tr 1 Mehmet Acikgoz 2 Department of the Basic Concepts of Engineering, Faculty of Engineering and Natural Sciences,ˇ¤IskenderunTechnical University, TR-31200 Hatay, Turkey University of Gaziantep, Faculty of Science and Arts, Department of Mathematics, TR-27310 Gaziantep,Turkey In this paper, we first provide the generalized degenerate Gould-Hopper polynomials via thedegenerate exponential functions and then give various relations and formulas such as addition formula andexplicit identity. Moreover, we consider the generalized Gould-Hopper based degenerate central factorialnumbers of the second kind and present several identities and relationships. Furthermore, we introducethe generalized Gould-Hopper based fully degenerate central Bell polynomials and investigated multifariouscorrelations and formulas including summation formulas, derivation rule and correlations with the Stirlingnumbers of the first kind, the generalized Gould-Hopper based degenerate central factorial numbers of thesecond kind and the generalized degenerate Gould-Hopper polynomials. We then acquire some relations withthe degenerate Bernstein polynomials for the generalized Gould-Hopper based fully degenerate central Bellpolynomials. Finally, we consider the Gould-Hopper based fully degenerate Bernoulli, Euler and Genocchipolynomials and by utilizing these polynomials, we develop some representations for the generalized Gould-Hopper based fully degenerate central Bell polynomials. http://pubs.sciepub.com/tjant/7/5/1/tjant-7-5-1.pdf Degenerate exponential function Central factorial numbers Central Bell polynomials Gould-Hopper polynomials Stirling numbers of the first kind