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Exact solutions of Schrodinger equation are obtained for the modified Kratzerand the corrected Morse potentials with the position-dependent effective mass.The bound state energy eigenvalues and the corresponding eigenfunctions arecalculated for any angular momentum for target potentials. Various forms ofpoint canonical transformations are applied. PACS numbers: 03.65.-w; 03.65.Ge;12.39.Fd Keywords: Morse potential, Kratzer potential, Position-dependent mass,Point canonical transformation, Effective mass Schr\"{o}dinger equation.

Exact solution of Schrodinger equation for modified Kratzer's molecular potential with the position-dependent mass