A mean-value Approach to solve fractional differential and integral equations

In this paper we provide a new numerical method to solve nonlinear fractional differential and integral equations. The algorithm proposed is based on an application of the fractional Mean-Value Theorem, which allows to transform the initial problem into a suitable system of nonlinear equations. The latter is easily solved through standard methods. We prove that the approximated solution converges to the exact (unknown) one, with a rate of convergence depending on the non-integer order characterizing the fractional equation. To test the effectiveness of our proposal, we produce several examples and compare our results with already existent procedures.