Caputo Nabla Fractional Boundary Value Problems and Integral Inequalities on Time Scales

In the first half of this work, we study boundary value problems with the Caputo nabla difference in the context of discrete fractional nabla calculus, especially when the right boundary condition has a fractional order. We first construct the Green’s function for the general case and study the properties of the Green’s function in several cases. We then apply the cone theory in Banach space to show the existence of positive solutions to a nonlinear boundary value problem. In the second half of the work, we study Feng-Qi type integral inequalities on time scales. We generalize some results for specific time scales to more general time scales