On neighborhoods of two new subclasses of multivalent functions with negative coefficients

In this paper, we introduce two new subclasses of p-valent analytic functions defined by means of fractional derivative of order δδ. We obtained the various results including coefficient bounds and distortion inequalities for these function classes. Furthermore, we determine some inclusion relations for the (n,p,ε)(n,p,ε)-neighborhoods of a family of p-valent analytic functions with negative coefficients which is defined by means of a certain nonhomogeneous Cauchy–Euler differential equation.