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In the generalized thermoelasticity with fractional order heat conduction and nonlocal elasticity, a generalized piezoelectric-thermoelastic problem of a both-end-fixed finite length piezoelectric rod with temperature-dependent properties and subjected to a moving heat source is investigated. The dimensionless governing equations are formulated and then solved by Laplace transform and its numerical inversion. In calculation, the effects of the nonlocal parameter, the fractional order parameter and the temperature-dependent properties on the non-dimensional temperature, displacement, stress and electrical potential are explored and demonstrated graphically. The results show that they significantly influence the peak value or magnitude of the considered physical variables.