Positivity DOI 10.1007/s11117-017-0504-y Positivity Commutators of fractional maximal operator on generalized Orlicz–Morrey spaces Fatih Deringoz 1 · Vagif S. Guliyev 1,2,3 · Sabir G. Hasanov 4 Received: 27 November 2016 / Accepted: 30 May 2017 © Springer International Publishing 2017 Abstract In the present paper, we shall give necessary and sufficient conditions for the Spanne and Adams type boundedness of the commutators of fractional maximal operator on generalized Orlicz–Morrey spaces, respectively. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators. Keywords Generalized Orlicz–Morrey space · Fractional maximal operator · Commutator · BMO Mathematics Subject Classification 42B25 · 42B35 · 46E30 The research of V.S. Guliyev and F. Deringoz is partially supported by the grant of Ahi Evran University Scientific Research Project (FEF.A3.16.024). The research of V.S. Guliyev is partially supported by the Ministry of Education and Science of the Russian Federation (the Agreement No. 02.a03.21.0008). B Fatih Deringoz deringoz@hotmail.com Vagif S. Guliyev vagif@guliyev.com Sabir G. Hasanov sabhasanov@gmail.com 1 Department of Mathematics, Ahi Evran University, Kirsehir, Turkey 2 S.M. Nikolskii Institute of Mathematics at RUDN University, 6 Miklukho-Maklay St, Moscow 117198, Russia 3 Institute of Mathematics and Mechanics, Baku, Azerbaijan 4 Ganja State University, Ganja, Azerbaijan