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.

A mean-value Approach to solve fractional differential and integral equations / De Angelis, Paolo; De Marchis, Roberto; Martire, Antonio Luciano; Oliva, Immacolata. - In: CHAOS, SOLITONS & FRACTALS. - ISSN 1873-2887. - 138:(2020). [10.1016/j.chaos.2020.109895]

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

Paolo De Angelis;Roberto De Marchis;Antonio Luciano Martire;Immacolata Oliva
2020

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.
2020
Fractional differential equation; Fractional Volterra integral equations; Mean-value theorem
01 Pubblicazione su rivista::01a Articolo in rivista
A mean-value Approach to solve fractional differential and integral equations / De Angelis, Paolo; De Marchis, Roberto; Martire, Antonio Luciano; Oliva, Immacolata. - In: CHAOS, SOLITONS & FRACTALS. - ISSN 1873-2887. - 138:(2020). [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/11573/1416721
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