具有广义调质分数阶拉普拉斯算子的变阶分数阶可合微分方程的极大值原理

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractal and Fractional Pub Date : 2023-11-01 DOI:10.3390/fractalfract7110798

Tingting Guan, Lihong Zhang

{"title":"具有广义调质分数阶拉普拉斯算子的变阶分数阶可合微分方程的极大值原理","authors":"Tingting Guan, Lihong Zhang","doi":"10.3390/fractalfract7110798","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate properties of solutions to a space-time fractional variable-order conformable nonlinear differential equation with a generalized tempered fractional Laplace operatorby using the maximum principle. We first establish some new important fractional various-order conformable inequalities. With these inequalities, we prove a new maximum principle with space-time fractional variable-order conformable derivatives and a generalized tempered fractional Laplace operator. Moreover, we discuss some results about comparison principles and properties of solutions for a family of space-time fractional variable-order conformable nonlinear differential equations with a generalized tempered fractional Laplace operator by maximum principle.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"9 11","pages":"0"},"PeriodicalIF":3.6000,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Maximum Principle for Variable-Order Fractional Conformable Differential Equation with a Generalized Tempered Fractional Laplace Operator\",\"authors\":\"Tingting Guan, Lihong Zhang\",\"doi\":\"10.3390/fractalfract7110798\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we investigate properties of solutions to a space-time fractional variable-order conformable nonlinear differential equation with a generalized tempered fractional Laplace operatorby using the maximum principle. We first establish some new important fractional various-order conformable inequalities. With these inequalities, we prove a new maximum principle with space-time fractional variable-order conformable derivatives and a generalized tempered fractional Laplace operator. Moreover, we discuss some results about comparison principles and properties of solutions for a family of space-time fractional variable-order conformable nonlinear differential equations with a generalized tempered fractional Laplace operator by maximum principle.\",\"PeriodicalId\":12435,\"journal\":{\"name\":\"Fractal and Fractional\",\"volume\":\"9 11\",\"pages\":\"0\"},\"PeriodicalIF\":3.6000,\"publicationDate\":\"2023-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractal and Fractional\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/fractalfract7110798\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractal and Fractional","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/fractalfract7110798","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

摘要

本文利用极大值原理研究了一类具有广义调质分数阶拉普拉斯算子的空时分数阶变阶可合非线性微分方程解的性质。首先建立了一些新的重要的分数阶可适应不等式。利用这些不等式，我们证明了一个新的时空分数阶变阶可调导数的极大原理和一个广义调质分数阶拉普拉斯算子。此外，利用极大值原理讨论了一类具有广义调质分数阶拉普拉斯算子的时空分数阶变阶可调非线性微分方程解的比较原理和性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Maximum Principle for Variable-Order Fractional Conformable Differential Equation with a Generalized Tempered Fractional Laplace Operator

In this paper, we investigate properties of solutions to a space-time fractional variable-order conformable nonlinear differential equation with a generalized tempered fractional Laplace operatorby using the maximum principle. We first establish some new important fractional various-order conformable inequalities. With these inequalities, we prove a new maximum principle with space-time fractional variable-order conformable derivatives and a generalized tempered fractional Laplace operator. Moreover, we discuss some results about comparison principles and properties of solutions for a family of space-time fractional variable-order conformable nonlinear differential equations with a generalized tempered fractional Laplace operator by maximum principle.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.60

自引率

18.50%

发文量

632

审稿时长

11 weeks

期刊介绍： Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.