Subclasses of spiral-like functions associated with the modified Caputo's derivative operator

In this paper, the authors apply the modified Caputo's derivative operator, to introduce two new subclasses of spiral-like functions, namely the spiral-starlike functions and spiral-convex functions. In addition to this we, elaborate on the inclusion properties of these subclasses by considering the generalization of the Mittag-Leffler function and its integral transformation. Consequently, we obtain the subordination result for the functions in the class of spiral-like functions.

Automated summary

In this paper, the modified Caputo's derivative operator is applied to introduce two new subclasses of spiral-like functions, namely the spiral-starlike functions and spiral-convex functions. The inclusion properties of these subclasses are elaborated by considering the generalization of the Mittag-Leffler function and its integral transformation. Consequently, the subordination result for the functions in the class of spiral-like functions is obtained.