This paper analyzes the electrostatic responses of polarly radially anisotropic (PRA) cylindrical shell and spherically radially anisotropic (SRA) spherical shell in presence of non-integer dimensional (NID) space. This is obtained by placing both of these geometries in space having non-integer dimensions. The influence of presence of NID space on cloaking and magnification using these geometries have been worked out. Observations have shown that PRA cylindrical shell can only yield cloaking by selecting certain anisotropy ratio in presence of NID space, whereas magnification cannot be achieved. Numerical simulations have been done to show the effectiveness of NID space and for difference of the presence of NID space and ordinary space. However, SRA spherical shell is independent of the presence of NID space for cloaking and magnification.
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