# Relativistic Heat Equation via L\'{e}vy stable distributions: Exact Solutions

@article{Penson2016RelativisticHE, title={Relativistic Heat Equation via L\'\{e\}vy stable distributions: Exact Solutions}, author={K. A. Penson and K. G{\'o}rska and A. Horzela and G. Dattoli}, journal={arXiv: Mathematical Physics}, year={2016} }

We introduce and study an extension of the heat equation relevant to relativistic energy formula involving square root of differential operators. We furnish exact solutions of corresponding Cauchy (initial) problem using the operator formalism invoking one-sided L\'{e}vy stable distributions. We note a natural appearance of Bessel polynomials which allow one the obtention of closed form solutions for a number of initial conditions. The resulting relativistic diffusion is slower than the non… CONTINUE READING

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