http://www.aimspress.com/journal/Math AIMS Mathematics, 6(11): 12680–12697. DOI:10.3934/math.2021731 Received: 19 July 2021 Accepted: 18 August 2021 Published: 06 September 2021 Research article A new family of degenerate poly-Bernoulli polynomials of the second kind with its certain related properties Waseem A. Khan 1, ∗ , Abdulghani Muhyi 2 , Rifaqat Ali 3 , Khaled Ahmad Hassan Alzobydi 3 , Manoj Singh 4 and Praveen Agarwal 5,6,7 1 Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O Box 1664, Al Khobar 31952, Saudi Arabia 2 Department of Mathematics, Hajjah University, Hajjah, Yemen 3 Department of Mathematics, College of Science and Arts, Muhayil, King Khalid University, P.O Box 9004, Postal Code:61413. Abha, Saudi Arabia 4 Department of Mathematics, College of Science, Jazan University, Jazan, Saudi Arabia 5 Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India 6 Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman AE 346, United Arab Emirates 7 International Center for Basic and Applied Sciences, Jaipur 302029, India * Correspondence: Email: wkhan1@pmu.edu.sa; Tel: +966569242353. Abstract: The main object of this article is to present type 2 degenerate poly-Bernoulli polynomials of the second kind and numbers by arising from modified degenerate polyexponential function and investigate some properties of them. Thereafter, we treat the type 2 degenerate unipoly- Bernoulli polynomials of the second kind via modified degenerate polyexponential function and derive several properties of these polynomials. Furthermore, some new identities and explicit expressions for degenerate unipoly polynomials related to special numbers and polynomials are obtained. In addition, certain related beautiful zeros and graphical representations are displayed with the help of Mathematica. Keywords: modified degenerate polyexponential functions; type 2 degenerate poly-Bernoulli polynomials of the second kind; degenerate unipoly functions Mathematics Subject Classification: 05A19, 11B73, 11B83