Fractional Powers of the Differentiation and Integration Operators and its Application in Accelerator Physics and Technology

In this paper we present a solution to a fractional integral of the order 3/2 with the use of a novel method. The integral arises during solving the Biot-Savart equation to find the exact analytical solution for the magnetic field components of a solenoid. We solved the integral by cutting the branch line in order to have an analytic function inside the integral instead of multi-valued operation.