Green's and Stoke's Theorems Redefined with SFVCP - Kankarej, Manisha; Singh, Jai Pratap (IAENG international journal of applied mathematics, 2025)
In this research we have explored the concept of circulation and flux of a vector field using the definition of standard fractional vector cross product(SFVCP). We have then applied this novel definition to Green's (tangential and normal form) and Stoke's theorem which has not been explored previously. Green's theorem is applied in context of complex variable to redefine Cauchy's Integral theorem. It is evident that for y = 1 all theorems reduces to standard theorems. The unique perspective of the paper lies in applying SFVCP to explain Green's and Stoke's theorem. It is evident that SFVCP offers more practical applications, accuracy and is more powerful in electromagnetic field and fluid mechanics, where they are used to relate field quantities over a region of space to those over its boundary, providing both conceptual insights and practical tools for solving physical problems.