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The dual-phase-lag thermoelasticity theory with the memory-dependent differential can perfectly describe the phenomenon of non-Fourier heat conduction, nevertheless, it has not been comprehensively considered: the mechanical responses of materials under the size-dependent effects and the multiphysics coupling effects such as magnetic, thermal and elastic fields. A modified dual-phase-lag thermoelasticity theory with memory-dependent effects and non-local effects was established. Based upon this theory, the magneto-thermoelastic coupling problem of narrow long thin plates subjected to cyclical heat sources was investigated. First, the governing equations for the problem were formulated. Then with the boundary conditions and initial conditions, the solution to the problem was obtained through the Laplace transform and the inverse transform techniques. Finally, the influences of the magnetic field, the phase lag, the time-delay, the kernel function, non-local effect and the time on the dimensionless quantities were investigated respectively. The work provides a powerful reference for the dynamic responses of micro-scale materials. [ABSTRACT FROM AUTHOR]