A class of fractional differential equations via power non-local and non-singular kernels: existence, uniqueness and numerical approximations
| Autor: | Zitane, Hanaa, Torres, Delfim F. M. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Phys. D 457 (2024), Art. 133951, 9 pp |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.physd.2023.133951 |
| Popis: | We prove a useful formula and new properties for the recently introduced power fractional calculus with non-local and non-singular kernels. In particular, we prove a new version of Gronwall's inequality involving the power fractional integral; and we establish existence and uniqueness results for nonlinear power fractional differential equations using fixed point techniques. Moreover, based on Lagrange polynomial interpolation, we develop a new explicit numerical method in order to approximate the solutions of a rich class of fractional differential equations. The approximation error of the proposed numerical scheme is analyzed. For illustrative purposes, we apply our method to a fractional differential equation for which the exact solution is computed, as well as to a nonlinear problem for which no exact solution is known. The numerical simulations show that the proposed method is very efficient, highly accurate and converges quickly. Comment: This is a preprint of a paper whose final form is published in 'Physica D: Nonlinear Phenomena' (ISSN 0167-2789). Submitted 19-Jan-2023; revised 15-May-2023; accepted for publication 11-Oct-2023 |
| Databáze: | arXiv |
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