At zero temperature, by obtaining linear electromagnetic response kernel of quasi-two dimensional FFLO d-wave superconductor subjected to additional applied magnetic field, due to nonlocal effect, penetration depth is calculated for both specular and diffuse boundaries. The results show that the nonlocal correction to the total response kernel of FFLO in the long wavelength limit is linear in external magnetic field characteristic vector (q) and this linearity is the same as a d-wave superconductor, but the part of kernel of FFLO, which depends on characteristic of FFLO state, is smaller than of usual d-wave superconductor, because of existing of Q.
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