ABSTRACT
In this chapter we study self-adjoint conformable dynamic equations on time scales. We investigate disconjugacy of self-adjoint equations and use corresponding Green's functions to study boundary value problems. We derive some reduction of order theorems. Dominant and recessive solutions are introduced, along with some of their properties. Further in this chapter, we introduce the Póolya factorization for a class conformable self-adjoint dynamic equations which we utilize for a variation of parameters for a class of nonhomogeneous conformable dynamic equations. We discuss the oscillation and disconjugacy of a certain class of second order homogeneous conformable dynamic equations. Also, the theory of Riccati equations is developed. We discuss the Cauchy function and derive a variation of constants formula for a class of conformable nonhomogeneous self-adjoint dynamic equations. Moreover, we investigate some periodic boundary value problems and their associated Green functions.
