Eigenspectra and thermodynamic quantities in graphene under the inside and outside magnetic fields

. In this research, firstly, the Dirac-Weyl equation has been solved for the bound states of a graphene quantum dot formed by the inhomogeneous distributions of the magnetic fields inside and outside the graphene quantum dot by using the series method. Then, we have obtained the density of states, electronic density and gate voltage using the obtained fermions energy. Also, we have calculated the wave function as the Hessenberg determinants from calculation of their elements. On the other hand, we have obtained of the thermodynamic quantities of the Dirac-Weyl fermions inside the graphene quantum dot. Finally, we have discussed on the obtained analytically results.