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http://hdl.handle.net/10773/39889
Title: | A class of fractional differential equations via power non-local and non-singular kernels: Existence, uniqueness and numerical approximations |
Author: | Zitane, Hanaa Torres, Delfim F. M. |
Keywords: | Fractional initial value problems Gronwall’s inequality Non-singular kernels Numerical methods Power fractional calculus |
Issue Date: | 2024 |
Publisher: | Elsevier |
Abstract: | 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. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/39889 |
DOI: | 10.1016/j.physd.2023.133951 |
ISSN: | 0167-2789 |
Publisher Version: | https://doi.org/10.1016/j.physd.2023.133951 |
Appears in Collections: | CIDMA - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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[547]Zitane_Torres_PHYSD-D.pdf | 1.07 MB | Adobe PDF | View/Open |
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