The Nature of the Solution for Cancerous Tumors Operator Equation

Abstract

In this paper, we study the solution of the cancerous tumors operator equation of the form:A^ast XA+t AXA=Q, Where A is a known operator defined on a Hilbert space H, represent the contributing factors are cancer (Hormonal factor ,Nutrient factor, Relationship between nutrient and hormone, Genetic factor, Viruses,...), Q is a known operator defined on a Hilbert space H, represent the percentages of contributing. Factors are cancer (Sex, Age, Exposure to radiation, Take sedatives, Psychological stress, Factors that weaken immunity, ...), t is any scalar positive real number, represent the control factor, X is unknown operator, represents the treatment of the injured in terms of quantity and quality of treatment , and A^ast is adjoint of operator A. Also, we show the nature of the solution for this operator equation for special types of operators. As well as, we will introduce some propositions and remarks because it is very important in this new study of medical systems of differential equations.