When defining a differential operator, one often employs, besides ordinary derivatives, generalized derivatives, which appear in a natural way when considering extensions of differential operators defined on differentiable functions, and weak derivatives, related to the transition to the adjoint operator [9]. Derivatives of fractional and negative orders appear when the differentiation is defin...

A partial differential operator associated with natural oscillations of an incompressible fluid in the neighbourhood of an elliptical flow is considered. The differentiation is only taken with respect to the angular variable, and thus the operator becomes a family of ordinary differential operators parametrized by the radial variable. It is shown that the spectra of these ordinary differential ...

Complete second-order hyperbolic differential equations with constant domains of operator coefficients were investigated in [1, 2]. In the case of variable domains of operator coefficients, second-order hyperbolic differential equations with a two-term leading part were analyzed in [3-5]. In the present paper, we investigate second-order hyperbolic differential equations with a three-term leadi...

In the present investigation, we use principle of subordination to introduce a new family for holomorphic functions defined by generalized differential operator. Also establish some interesting geometric properties belonging this family.