Study on the Importance of Functional and Neutral Differential Equation Branch Algebra

Exploring Nonlinear Differential and Integral Equations in Banat Algebras

Abstract

It is well-known that most of the natural and physical Phenomena in the universe are not straight forward and hence are modeled on the systems of nonlinear equations. Again, almost all such natural and physical phenomena involve the decay or growth that is the change in the state with respect to the time period. So such dynamical systems in the universe are governed by the nonlinear differential and integral equations. The initial and boundary value problems of first and second order ordinary nonlinear differential equations have attracted the attention of several mathematicians of the world since long time and much has been done concerning the various aspects of the solutions for nonlinear differential equations. Similar is the case with nonlinear integral equations. In the present thesis, we have dealt with initial value problems of some nonlinear first and second order ordinary differential equations in Banat algebras. Furthermore, some nonlinear integral equations in Banat algebras involving the more than one nonlinearity are also discussed for various aspects of the solutions