Nonlinear higher order functional random differential equations

Abstract

Presently the theory of nonlinear functional differential equation is a very active area of mathematical research and applications of theory are of fundamental importance in the formulation and analysis of various classes of operators equation which arise in the physical, biological, engineering and technological sciences. Usually the mathematical models or the equations that have been used to describe a particular phenomenon or process of the universe contain a certain parameter, which has some specific physical interpretation, but whose value is not known. If any such phenomena involving so mentioned parameter and which satisfy certain probabilistic or measure theoretic behavior with respect to the parameter, then we say it is a random phenomenon. For example, in the theory of diffusion or heat- condition we have the diffusion co-efficient or the co-efficient of conductivity play the prominent role in the said phenomena. Similarly in the wave theory, the propagation coefficient and in the theory of elasticity, the modules of elasticity play the significant role in the behavior of the underlined process. The coefficient or parameters are generally determined by experimentally that is, by taking the mean value by several observations. Hence when we talk about some parameters are coefficients, the random analysis of the random equation is evident, and so the random equations have been studied in the literature, since long time, by the various mathematicians all over the world. Thus the study of natural or physical phenomena with the help of random models or equation forms an important branch of the nonlinear analysis and some details of random. newlineThen theory of random equations still in its primitive stage, however there is a very extensive literature available dealing with the following four basic classes of random analysis. newlinei) Random algebraic equations. newlineiv newlineii) Random difference equations. newlineiii) Random integral equations. newlineiv) Random differential equations.