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

Paolo De Angelis, Roberto De Marchis, Antonio Luciano Martire and Immacolata Oliva

Chaos, Solitons & Fractals, 2020, vol. 138, issue C

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.

Keywords: Fractional differential equation; Fractional Vvolterra integral equations; Mean-value theorem (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920302952

DOI: 10.1016/j.chaos.2020.109895

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