Unpolarized QED parton distribution functions in NLO

Perturbative solutions for unpolarized QED parton distribution and fragmentation functions are presented explicitly in the next-to-leading logarithmic approximation. The scheme of iterative solution of QED evolution equations is described in detail. Terms up to $\mathcal{O}({\alpha }^3{L}^2)$ are calculated analytically, where $L=\ln ({\mu }_F^2\mathrm{/}{m}_e^2)$ is the large logarithm which depends on the factorization energy scale ${\mu }_F\gg m_e$. The results are process independent and relevant for future high-precision experiments.