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. (c) 2020 Elsevier Ltd. All rights reserved.

De Angelis, P., De Marchis, R., Martire, A.L., Oliva, I. (2020). A mean-value Approach to solve fractional differential and integral equations. CHAOS, SOLITONS AND FRACTALS, 138 [10.1016/j.chaos.2020.109895].

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

#### Abstract

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. (c) 2020 Elsevier Ltd. All rights reserved.
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2020
De Angelis, P., De Marchis, R., Martire, A.L., Oliva, I. (2020). A mean-value Approach to solve fractional differential and integral equations. CHAOS, SOLITONS AND FRACTALS, 138 [10.1016/j.chaos.2020.109895].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11590/425842`
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