Existence, Uniqueness and Successive Approximations for Caputo Tempered Fractional Differential Equations

Nawal Bettayeb; Abdelkrim Salim; Jamal Eddine Lazreg; Mouffak Benchohra

doi:10.2478/tmmp-2025-0022

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Existence, Uniqueness and Successive Approximations for Caputo Tempered Fractional Differential Equations

Tatra Mountains Mathematical Publications

Volume 90 (2025): Issue 2 (December 2025)

By: Nawal Bettayeb, Abdelkrim Salim, Jamal Eddine Lazreg and Mouffak Benchohra

Open Access

|Dec 2025

Abstract

This study aims to analyze the global convergence and uniqueness properties of the successive approximations method when applied to Caputo tempered fractional differential equations. We provide rigorous mathematical proofs to establish the convergence of the method, ensuring that the iterative process converges to a unique solution. Furthermore, we investigate the impact of the nonlocal conditions on the uniqueness of the solution obtained through the successive approximations method.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2025-0022 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 35 - 50

Submitted on: Jun 15, 2023

Accepted on: Aug 23, 2025

Published on: Dec 18, 2025

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

the Caputo tempered fractional derivative,

global convergence,

uniqueness,

successive approximations,

nonlocal conditions

Related subjects:

Mathematics,

General mathematics

© 2025 Nawal Bettayeb, Abdelkrim Salim, Jamal Eddine Lazreg, Mouffak Benchohra, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 90 (2025): Issue 2 (December 2025)