Tempered Fractional Dirac Type Systems

Abstract

In this research, we present a boundary value problem for a Dirac
a system using Caputo-type tempered fractional derivatives, a 2-dimensional
and less than one linear fractional differential equation system. 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.