Fractional-Diffraction-Optics Cauchy Problem: Resolvent-Function Solution of the Matrix Integral Equation
arxiv(2024)
摘要
The fractional diffraction optics theory has been elaborated using the Green
function technique. The optics-fractional equation describing the diffraction
X-ray scattering by imperfect crystals has been derived as the fractional
matrix integral Fredholm–Volterra equation of the second kind. In the paper,
to solve the Cauchy problems, the Liouville–Neumann-type series formalism has
been used to build up the matrix Resolvent-function solution. In the case when
the imperfect crystal-lattice elastic displacement field is the linear function
f( R) = a x+b, a, b = const, the explicit solution of the
diffraction-optics Cauchy problem has been obtained and analyzed for arbitrary
fractional-order-parameter α, α∈ (0, 1].
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