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EnglishIn 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]
| Titolo: | A mean-value Approach to solve fractional differential and integral equations | |
| Data di pubblicazione: | 2020 | |
| Autori: | ||
| Stringa autori: | De Angelis, Paolo; De Marchis, Roberto; Martire, Antonio Luciano; Oliva, Immacolata | |
| Numero degli autori: | 4 | |
| Nazionalità autore: | ITALIA | |
| Lingua: | Inglese | |
| Rivista: | CHAOS, SOLITONS & FRACTALS | |
| Revisione (peer review): | Esperti anonimi | |
| Volume: | 138 | |
| Numero articolo: | 109895 | |
| Numero di pagine: | 8 | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.chaos.2020.109895 | |
| Codice identificativo Scopus: | 2-s2.0-85086501355 | |
| Codice identificativo ISI: | WOS:000571059300001 | |
| 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. | |
| Parole Chiave: | Fractional differential equation; Fractional Volterra integral equations; Mean-value theorem | |
| Appartiene alla tipologia: | 01a Articolo in rivista |
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http://hdl.handle.net/11573/1416721
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