Linear and Higher Order Fractional Operator with SFVCP

In this research, fractionalizing of linear operator with Standard Fractional Vector Cross Product (SFVCP) in Euclidean 3 – space has been defined. The fractional parameter γ describes the order of the fractional curl operator. For values of 0 < γ < 1, fractional solutions are considered as intermediate states between solution and its dual. This research plays a key role in understanding the relation between the field and its dual field. Solutions obtained in this research indicate that understanding of more complex problems in electromagnetic wave propagation and field interaction is smooth with use of SFVCP. Fractional solutions for the real values of fractional parameters which are greater than unity are also a part of this study. This research is the first application of standard fractional vector cross product to find the solution for Maxwell’s equation. The results obtained in this research have further applications in identifying the interaction of electric and magnetic fields, areas of wireless communication, radar systems and design of new electromagnetic devices.