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In the fractional nonrelativistic potential model, the decomposition of heavy quarkonium in a hot magnetized medium is investigated. The analytical solution of the fractional radial Schrodinger equation for the hot-magnetized ¨ interaction potential is displayed by using the conformable fractional Nikiforov-Uvarov method. Analytical expressions for the energy eigenvalues and the radial wave function are obtained for arbitrary quantum numbers. Next, we study the charmonium and bottmonium binding energies for different values of the magnetic field in the thermal medium. The effect of the fractional parameter on the decomposition temperature is also analyzed for charmonium and bottomonium in the presence of hot magnetized media. We conclude that the dissociation of heavy quarkonium in the fractional nonrelativistic potential model is faster than the classical nonrelativistic potential model. [ABSTRACT FROM AUTHOR]