The paper develops structures on Hom-Lie algebroids and Hom-Courant algebroids.
problem Exploring new algebraic structures on Hom-Lie algebroids and Hom-Courant algebroids.
method Introducing Hom-Poisson, Hom-Nijenhuis, and Hom-Poisson-Nijenhuis structures on Hom-Lie algebroids and Hom-Dirac structures on Hom-Courant algebroids.
result Established properties and relationships among these structures, including a hierarchy and correspondence.