Generalized fractional Dirac type operators

TL;DR

This paper introduces a new class of fractional Dirac operators with variable coefficients, providing explicit solutions to related Cauchy problems and methods for inverse fractional wave and heat equations.

Contribution

It develops a novel framework combining fractional derivatives and variable coefficients for Dirac operators, with explicit solutions and inverse problem techniques.

Findings

Explicit solutions for fractional Cauchy problems

Method for recovering variable coefficient solutions

Illustrative examples demonstrating the approach

Abstract

We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian-Caputo fractional derivative and the fractional Laplacian, both operators defined with respect to some given functions. Direct and inverse fractional Cauchy type problems are studied for the introduced operators. We give explicit solutions of the considered fractional Cauchy type problems. We also use a recent method to recover a variable coefficient solution of some inverse fractional wave and heat type equations. Illustrative examples are provided.