Fractional order boundary value problems on time scales

This thesis consists of three main parts. In the first part, the problem was introduced. In the second part, the basic definitions and theorems related to time scale, beta-fractional derivative and beta-fractional integral were given. In the third part, the necessary definitions and lemmas for the existence of solutions were given. Then, the boundary value problem was reduced to the integral equation and the existence of at least one, two and three positive solutions proved by using Four Functionals Fixed Point Theorem, the Avery Henderson Fixed Point Theorem and the Five Functionals Fixed Point Theorem, respectively. Finally, examples were given to show that the obtained conditions are satisfiable.