Semi-integration of certain algebraic expressions

The theory of fractional calculus developed rapidly as the applications of this branch are extensive nowadays. There is no discipline of modern engineering and science that remains untouched by the techniques of fractional calculus. In fact, one could argue that real world processes are fractional order systems in general. In this article, we obtain the semi-integrals of certain algebraic functions in terms of difference of two complete elliptic integrals of different kinds by using series manipulation technique.