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Paper detail

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.

preprint2020arXivOpen access
Mostafa BehtoueiLuigi FaillaceLuigi PalumboBruno SpataroAlessandro VariolaMauro Migliorati
math-phphysics.acc-phmath.MPmath.CA
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Mostafa BehtoueiLuigi FaillaceLuigi PalumboBruno SpataroAlessandro VariolaMauro Migliorati

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