Relativistic equations with fractional and pseudo-differential operators

TL;DR

This paper explores solving partial differential equations with fractional and pseudo-differential operators, applying the methods to generalized heat equations and discussing extensions to relativistic quantum equations.

Contribution

It introduces techniques from fractional calculus to solve PDEs with non-integer operators and discusses their potential application to relativistic quantum equations.

Findings

Solutions to generalized heat equations using fractional operators

Potential extension to relativistic Schrödinger and Dirac equations

Framework for applying fractional calculus to relativistic PDEs

Abstract

In this paper we use different techniques from the fractional and pseudo-operators calculus to solve partial differential equations involving operators with non integer exponents. We apply the method to equations resembling generalizations of the heat equations and discuss the possibility of extending the procedure to the relativistic Schr\"odinger and Dirac equations.