New Certain Results of a Linear Multiplier Fractional q-Differintegral Operator for Fuzzy Differential Subordination and Superordination

The concept of fuzzy differential subordination was introduced in 2011 as a natural generalization of classical differential subordination, reflecting the contemporary trend of incorporating fuzzy set theory into well-established mathematical frameworks. This work aims to explore multiple fuzzy differential subordinations (FDS) and fuzzy differential superordinations (FDSs) associated with the linear multiplier fractional q-differintegral operator. Utilizing the linear multiplier fractional q-differintegral operator, we introduce a novel fuzzy subclass of analytic functions, denoted by SDFσ,m(q,λ,γ). Using the concept of FDS and FDSs, we identify important characteristics and analytical aspects of the class SDFσ,m(q,λ,γ). Furthermore, we derive a collection of FDS and FDSs results specifically related to the linear multiplier fractional q-differintegral operator.