The Iterative Properties for Positive Solutions of a Tempered Fractional Equation-Reference-Cited by-同舟云学术

The Iterative Properties for Positive Solutions of a Tempered Fractional Equation

Published:2023-10-16 Issue:10 Volume:7 Page:761
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Zhang Xinguang¹²^ORCID,Chen Peng¹,Tian Hui¹,Wu Yonghong²^ORCID

Affiliation:

1. School of Mathematical and Informational Sciences, Yantai University, Yantai 264005, China

2. Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia

Abstract

In this article, we investigate the iterative properties of positive solutions for a tempered fractional equation under the case where the boundary conditions and nonlinearity all involve tempered fractional derivatives of unknown functions. By weakening a basic growth condition, some new and complete results on the iterative properties of the positive solutions to the equation are established, which include the uniqueness and existence of positive solutions, the iterative sequence converging to the unique solution, the error estimate of the solution and convergence rate as well as the asymptotic behavior of the solution. In particular, the iterative process is easy to implement as it can start from a known initial value function.

Funder

Natural Science Foundation of Shandong Province of China

ARC Discovery Project Grant

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/10/761/pdf

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