We introduce a new class of functions, present their basic properties, and explain operations with those functions, including algebraic operations and operations of generalized calculus. We also provide illustrative examples of possible applications of our mathematical approach to modeling real materials of various kinds. In order to make the new tools applicable in various fields of science and engineering, including advanced modeling of real materials structure and behavior, calculations and manipulations with the introduced class of functions are implemented in the form of a toolbox for MATLAB.