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In this presentation, the author studies a fractional integro-differential equation with Caputo derivative and initial condition. The forcing function is the sum of an increasing and a decreasing function, and both the derivatives and integrals are of fractional order. In order to develop the main result, the author states definitions of lower and upper solutions of the IVP, and then develops monotone iterative techniques, where the iterates are solutions of linear Caputo integro-differential IVPs that converge uniformly and monotonically to minimal and maximal solutions of the main problem.