The purpose of this paper is to find new inclusion relations of the harmonic class $\mathcal{HF}(\varrho ,\gamma )$ with the subclasses ${\mathcal{S}}_{\mathcal{HF}}^{*},$${\mathcal{K}}_{\mathcal{HF}}$ and $\mathcal{T}{\mathfrak{N}}_{\mathcal{HF}}\left(\tau \right)$ of harmonic functions by applying the convolution operator $\Theta (\Im )$ associated with the Mittag-Leffler function. Further for $\varrho =0$, several special cases of the main results are also obtained.

In this study, the connection between certain subfamilies of harmonic univalent functions is established by utilizing a convolution operator involving the Mittag–Leffler function. The investigation reveals inclusion relations concerning harmonic $\gamma$-uniformly starlike mappings in the open unit disc, harmonic starlike functions and harmonic convex functions, highlighting the improvements given by the results presented here on previously published outcomes.

Here in this paper, we establish the basic inclusion relations among the harmonic class $\mathbb{HF}(\sigma ,\eta )$ with the classes $S_{\mathcal{HF}}^{*}$ of starlike harmonic functions and $K_{\mathcal{HF}}$ of convex harmonic functions defined in open symmetric unit disk U. Moreover, we investigate inclusion connections for the harmonic classes $\mathcal{T}{\mathfrak{N}}_{\mathbb{HF}}\left(\varrho \right)$ and $\mathcal{T}{\mathfrak{Q}}_{\mathbb{HF}}\left(\varrho \right)$ of harmonic functions by applying the operator $\mathrm{\Lambda }$ associated with the Bessel function. Furthermore, several special cases of the main results are obtained for the particular case $\sigma =0$.