Please use this identifier to cite or link to this item: 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

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