The resistivity properties are needed to solve induction heating while the thermal expansion coefficient is needed to solve the mechanical response due to heating.  The first problems is best solved in Abaqus using coupled thermal-electrical analysis, while the second may me solved separately, after having the solution of the first, with a separate stress analysis; or a coupled thermal-stress analysis may be done when a mutual influence is expected -as when large deformations under thermal load occurs.

Abaqus uses electrical conductivity properties, which are the reciprocal of resistivity, so instead of looking for resistivity in the manuals, look for electrical conductivity (distinct from thermal conductivity) as in the *ELECTRICAL CONDUCTIVITY keyword.  The thermal expansion coefficient is specified with the *EXPANSION keyword.  The is whole collection of example problems in Abaqus where you should start by finding problems that look like yours in a simple form, that has all the appropriate input required. 

That was really helpful. Thank you very much Leonard Oremont.