Existence and Uniqueness of Solutions to Proper Fractional Riemann-Liouville Initial Value Problems on Time Scales

doi:10.1201/9781003388678-13

Chapter

Existence and Uniqueness of Solutions to Proper Fractional Riemann-Liouville Initial Value Problems on Time Scales

ABSTRACT

Inspired in [Appl. Math. Lett. 121 (2021), Paper No. 107407], we study several properties of new Riemann-Liouville fractional operators on time scales. Then we prove sufficient conditions for a nonlinear Riemann-Liouville fractional initial value problem on an arbitrary time scale to have a solution, as well as sufficient conditions for the uniqueness of solution.