Abstract
The theory of pseudo-differential operators is a powerful tool to deal with differential equations involving differential operators under the square root sign. These types of equations are pivotal elements to treat problems in anomalous diffusion and in relativistic quantum mechanics. In this paper, we report on new links between fractional diffusion, quantum relativistic equations, and particular families of polynomials, linked to the Bessel polynomials in Carlitz form and playing the role of relativistic heat polynomials. We introduce generalizations of these polynomial families and point out their specific use for the solutions of problems of practical importance.
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