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

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