Meshless Method for solving the Conformable Fractional Maxwell Equations

The meshless method is proposed to obtain the approximate so- lution of the fractional Maxwell equations of a general conformable fractional derivative (GCFD), which is given to describe the elec- tromagnetic fields of inhomogeneous media or materials with local properties. The explicit method is applied to approximate the time variable. The radial point interpolation method (RPIM) with poly- nomial basis functions is used for discretizing the space variables and constructing the shape functions. The Kronecker delta function is used for the test function. The fractional transverse electric (TE) and the fractional transverse magnetic (TM) polarizations are presented to show the efficiency of the proposed method and to show the be- havior of the numerical solutions when adjusting the fractional order to be less than one. The oscillation and amplitude increase when the fractional order is reduced, and these changes affect the electric fields
more than the magnetic fields.