Study of Uniqueness and Ulam-Type Stability of Abstract Hadamard Fractional Differential Equations of Sobolev Type via Resolvent Operators

被引：4

作者：

Ould Melha, Khellaf ^{[1
]}

Mohammed Djaouti, Abdelhamid ^{[2
]}

Latif, Muhammad Amer ^{[2
]}

Chinchane, Vaijanath L. ^{[3
]}

机构：

[1] Hassiba Benbouali Univ, Fac Exact Sci & Informat, Dept Math, Ouled Fares 02180, Chlef, Algeria

[2] King Faisal Univ, Fac Sci, Dept Math, Al Hufuf 31982, Al Ahsa, Saudi Arabia

[3] Deogiri Inst Engn & Management Studies, Dept Math, Sambhajinagar 431005, India

来源：

AXIOMS | 2024年 / 13卷 / 02期

关键词：

Hadamard fractional derivative; Sobolev equation; resolvent operators; Ulam-Hyers-Rassias stability; EXISTENCE;

D O I：

10.3390/axioms13020131

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper focuses on studying the uniqueness of the mild solution for an abstract fractional differential equation. We use Banach's fixed point theorem to prove this uniqueness. Additionally, we examine the stability properties of the equation using Ulam's stability. To analyze these properties, we consider the involvement of Hadamard fractional derivatives. Throughout this study, we put significant emphasis on the role and properties of resolvent operators. Furthermore, we investigate Ulam-type stability by providing examples of partial fractional differential equations that incorporate Hadamard derivatives.

引用

页数：16

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