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In this paper the problem of gravitational deflection of relativistic chargedmassive particles in slowly rotating Kerr-Newman black holes is considered.Toward this purpose we have used two methods: Firstly, we have applied theGauss-Bonnet theorem (GBT) and the optical geometry to evaluate the deflectionangle of charged particles. Secondly, we have presented a detailed analysis ofthe deflection angle by means of the Hamilton-Jacobi equation recovering thesame invariant result for the deflection angle in leading order terms. Thecrucial point behind the first method is to use the correspondence between themotion of a charged massive particles in a gravitational field in presence ofelectromagnetic field and the motion of photons in a non-homogeneous coldplasma. It is shown that the deflection angle besides the black hole (BH) mass$M$, BH angular momentum $a$, BH electric charge $Q^2$, BH magnetic charge$P^2$, it is also affected by the electric charge of the particle $q$ andrelativistic velocity of the particle $v$.

Deflection angle of charged massive particles in slowly rotating Kerr-Newman space-times via Gauss-Bonnet theorem and Hamilton-Jacobi method