In this paper, we have considered a class of constrained non-smooth multiobjective fractional programming problem involving support functions under generalized convexity. Also, second order Mond Weir type dual and Schaible type dual are discussed and various weak, strong and strict converse duality results are derived under generalized class of second order (F, ${alpha}$, ${ ho}$, $d$)-V-type I functions. Also, we have illustrated through non-trivial examples that class of second order (F, ${alpha}$, ${ ho}$, $d$)-V-type I functions extends the definitions of generalized convexity appeared in the literature.