A New Family of Chain Function

Abstract

The simulation of the systems required to a mathematic functions, these functions are the arms of the mathematics in the engineering fields and they are used to describe the elements and relations of the systems. This paper proposed a new function annex to the mathematics library to increases the flexibility of the work in the engineering fields; this function is called Dhafer's function. The main structure for Dhafer's function is an empty function called the mother equation, it is continues piecewise with chain form. The mother equation will charged in optional operations to generate a family of functions. These functions are inherent the properties of the mother equation also each element in this family has its special properties. This family of functions has a large amount of advantages over the known functions to day. The mother equation has three sections the first one is the positive section that is a function to the instantaneous value of the independent variable and the previous value of the function connected by general operator that will call Dhafer operator. The second part is any suitable inverse for the positive section, while the third section is the initial part that is a simple function or constant value that connects the first and the second parts of the function. Some functions in this family have distinct properties such as the continuous factorial and the very fast growing function. The generalization and universe of these equations in the general form called Dhafer's chain function family.