Fractional calculus has proved its worth in engineering and as well as in medicine, analyzing papilloma-virus infection, typhoid fever, myelogenous leukemia, monkeypox, dengue infection, hand–foot–mouth disease, zika virus, and lymphatic filariasis infection. Fractal sets famous for their complex geometric features have gained remarkable attention in the last few decades due to their applications in image processing, data compression, and signal analysis. Our work merges fractional calculus, fractal sets, convexity and integral inequalities to get a broader perspective of this area of research. The main goal of this study is to introduce a new notation for harmonically convex mappings Formula: see text called generalized Formula: see text-exponential type Formula: see text over fractal space settings using Raina’s mapping. Various fractional variants of Hermite–Hadamard-type inequalities Formula: see text for this novel generalization cover the main section of this research. The graphical representations of the main results empower their validity. Finally, connecting findings with applications and the classical Mittag-Leffler mapping makes the study more enjoyable.
CHEN et al. (2025) studied this question.