Given a fermion or boson with an arbitrary integer or half integer spin, then what would be its Dirac or Klein-Gordon equation?
Dirac equation for an equation with arbitrary spin 0, 1/2 , 1 , 2 , 3/2 , and so on
Also, if supersymmetry is correct, then what would be the relation of an equation of a particle with spin $d$ and its corresponding super partner with spin $d-1/2$?
Eqs of motion for arbitrary spin massive field are given in this answer. Massless case can be also explocitly treated in a such way.
Briefly, equations of motion for field which represents the given elementary particle may be obtained from the statement that particles realizes unitary irreducible representations of Poincare group. As we know, for the irreducible representations Casimir operators acts as unity matrix, so by rewriting Casimir operators in differential form you obtain equations.
