Existence of Positive Solutions of a Fractional Dynamic Equation Involving Integral Boundary Conditions on Time Scales

Abstract

The existence and uniqueness of positive solutions to a fractional dynamic equation involving integral boundary conditions on time scale are examined using the Banach fixed point theorem and Schauder’s fixed point theorem. The existence of the proposed dynamic equation has been determined using the Caputo nabla derivative operator (Caputo derivative on time scale in the nabla sense), the upper and lower solution approach, and the characteristics of the Green’s function on time scales. Further, some appropriate examples has been given to demonstrate the implementation of theoretical results.