Fuzzy differential subordination and superordination results for the Mittag-Leffler type Pascal distribution

In this paper, we derive several fuzzy differential subordination and fuzzy differential superordination results for analytic functions ${\mathcal{M}}_{\xi ,\beta }^{s,\gamma }$, which involve the extended Mittag-Leffler function and the Pascal distribution series. We also investigate and introduce a class ${\mathcal{M}\mathcal{B}}_{\xi ,\beta }^{F,s,\gamma }(\rho )$ of analytic and univalent functions in the open unit disc $\mathcal{D}$ by employing the newly defined operator ${\mathcal{M}}_{\xi ,\beta }^{s,\gamma }$. We determine a specific relationship of inclusion for this class. Further, we establish prerequisites for a function role in serving as both the fuzzy dominant and fuzzy subordinant of the fuzzy differential subordination and superordination, respectively. Some novel results that are sandwich-type can be found here.