Duality of fractional derivatives: On a hybrid and non-hybrid inclusion problem

IF 0.9 4区 数学 Q2 MATHEMATICS
Leyla Soudani, Abdelkader Amara, Khaled Zennir, Junaid Ahmad
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引用次数: 0

Abstract

The main goal of this paper is to investigate a newly proposed hybrid and hybrid inclusion problem consisting of fractional differential problems involving two different fractional derivatives of order μ, Caputo and Liouville–Riemann operators, with multi-order mixed Riemann–Liouville integro-derivative conditions. Although α is between one and two, we need three boundary value conditions to find the integral equation. The study investigates the results of existence for hybrid, hybrid inclusion, and non-hybrid inclusion problems by employing several analytical approaches, including Dhage’s technique, α - ψ {\alpha-\psi} -contractive mappings, fixed points, and endpoints of the product operators. To further illustrate our findings, we present three examples.
分数导数的对偶性:关于混合与非混合包含问题
本文的主要目的是研究一个新提出的混合和混合包含问题,该问题由涉及两个阶数为μ的不同分数导数的分数微分问题、卡普托算子和黎曼-黎维尔算子组成,具有多阶混合黎曼-黎维尔积分-导数条件。虽然 α 介于一到二之间,但我们需要三个边界值条件来求得积分方程。本研究通过使用几种分析方法,包括 Dhage 技术、α - ψ {\alpha-\psi} -contractive 映射、定点和乘积算子的端点,研究了混合、混合包含和非混合包含问题的存在性结果。为了进一步说明我们的发现,我们举了三个例子。
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来源期刊
Journal of Inverse and Ill-Posed Problems
Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
2.60
自引率
9.10%
发文量
48
审稿时长
>12 weeks
期刊介绍: This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following topics are covered: Inverse problems existence and uniqueness theorems stability estimates optimization and identification problems numerical methods Ill-posed problems regularization theory operator equations integral geometry Applications inverse problems in geophysics, electrodynamics and acoustics inverse problems in ecology inverse and ill-posed problems in medicine mathematical problems of tomography
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