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http://hdl.handle.net/10773/32623
Title: | Approximate iterative method for initial value problem of impulsive fractional differential equations with generalized proportional fractional derivatives |
Author: | Agarwal, Ravi P. Hristova, Snezhana O’Regan, Donal Almeida, Ricardo |
Keywords: | Riemann–Liouville proportional fractional derivative Differential equations Impulses Initial value problem Lower solutions Upper solutions Monotone-iterative technique |
Issue Date: | 2-Aug-2021 |
Publisher: | MDPI |
Abstract: | The main aim of the paper is to present an algorithm to solve approximately initial value problems for a scalar non-linear fractional differential equation with generalized proportional fractional derivative on a finite interval. The main condition is connected with the one sided Lipschitz condition of the right hand side part of the given equation. An iterative scheme, based on appropriately defined mild lower and mild upper solutions, is provided. Two monotone sequences, increasing and decreasing ones, are constructed and their convergence to mild solutions of the given problem is established. In the case of uniqueness, both limits coincide with the unique solution of the given problem. The approximate method is based on the application of the method of lower and upper solutions combined with the monotone-iterative technique. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/32623 |
DOI: | 10.3390/math9161979 |
Publisher Version: | https://www.mdpi.com/2227-7390/9/16/1979 |
Appears in Collections: | CIDMA - Artigos DMat - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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mathematics-09-01979-v2.pdf | 349.7 kB | Adobe PDF | View/Open |
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