Generalized m -preinvexity on fractal set and related local fractional integral inequalities with applications

In this work, we address and explore the concept of generalized \(m\)-preinvex functions on fractal sets along with linked local fractional integral inequalities. Additionally, some engrossing algebraic properties are presented to facilitate current initiated idea. Furthermore, prove latest variant Hermite-Hadamard type inequality employing proposed definition preinvexity. We also derive several novel versions inequalities Fejér-Hermite-Hadamard for first-order differentiable functions. Finally, new means random variables established as applications.