Tempered fractional Dirac type systems

Abstract

In this research, we present a boundary value problem for a Dirac system with tempered fractional derivatives. Firstly, the definitions and properties of tempered fractional derivatives and tempered fractional integrals are given. Next, it is shown that the operator of the corresponding eigenvalue problem is a self-adjoint operator, that the eigenfunctions are orthogonal concerning different eigenvalues, and in which case the eigenvalue is simple.