A study on the existence results of boundary value problems of fractional relaxation integro-differential equations with impulsive and delay conditions in Banach spaces

被引：4

作者：

Chasreechai, Saowaluck ^{[1
,2
]}

Poornima, Sadhasivam ^{[3
]}

Karthikeyann, Panjaiyan ^{[3
]}

Karthikeyan, Kulandhaivel ^{[4
]}

Kumar, Anoop ^{[5
]}

Kaushik, Kirti ^{[5
]}

Sitthiwirattham, Thanin ^{[2
,6
]}

机构：

[1] King Mongkuts Univ Technol North Bangkok, Fac Appl Sci, Dept Math, Bangkok 10800, Thailand

[2] King Mongkuts Univ Technol North Bangkok, Sci & Technol Res Inst, Res Grp Fract Calculus Theory & Applicat, Bangkok 10800, Thailand

[3] Sri Vasavi Coll, Dept Math, Erode 638136, India

[4] KPR Inst Engn & Technol, Dept Math, Coimbatore 641407, Tamil Nadu, India

[5] Cent Univ Punjab, Dept Math & Stat, Bathinda, Punjab, India

[6] Suan Dusit Univ, Fac Sci & Technol, Math Dept, Bangkok 10300, Thailand

来源：

AIMS MATHEMATICS | 2024年 / 9卷 / 05期

关键词：

Riemann-Liouville fractional derivative; fractional relaxation impulsive integro; di fferential equations; Liouville-Caputo fractional derivative; existence; uniqueness; delay; fixed point; UNIQUENESS;

D O I：

10.3934/math.2024563

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper was to provide systematic approaches to study the existence of results for the system fractional relaxation integro-differential equations. Applied problems require definitions of fractional derivatives, allowing the utilization of physically interpretable boundary conditions. Impulsive conditions serve as basic conditions to study the dynamic processes that are subject to sudden changes in their state. In the process, we converted the given fractional differential equations into an equivalent integral equation. We constructed appropriate mappings and employed the Schaefer's fixed-point theorem and the Banach fixed-point theorem to show the existence of a unique solution. We presented an example to show the applicability of our results.

引用

页码：11468 / 11485

页数：18

共 26 条

[11] Caputo-Hadamard implicit fractional differential equations with delay [J].

Krim, Salim ;

Abbas, Said ;

Benchohra, Mouffak .

SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2021, 15 (01) :463-484

[12] The analysis of a time delay fractional COVID-19 model via Caputo type fractional derivative [J].

Kumar, Pushpendra ;

Suat Erturk, Vedat .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (07) :7618-7631

[13] EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR FRACTIONAL RELAXATION INTEGRO-DIFFERENTIAL EQUATIONS WITH BOUNDARY CONDITIONS [J].

Lachouri, Adel ;

Ardjouni, Abdelouaheb ;

Djoudi, Ahcene .

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2022, 37 (01) :211-221

[14]

Liu M., 2023, WAVE RANDOM COMPLEX, P1, DOI DOI 10.1080/17455030.2023.2176695

[15] Existence of ahnost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay [J].

Ma, Xiao ;

Shu, Xiao-Bao ;

Mao, Jianzhong .

STOCHASTICS AND DYNAMICS, 2020, 20 (01)

[16] Existence, uniqueness and approximation of nonlocal fractional differential equation of sobolev type with impulses [J].

Manjula, M. ;

Kaliraj, K. ;

Botmart, Thongchai ;

Nisar, Kottakkaran Sooppy ;

Ravichandran, C. .

AIMS MATHEMATICS, 2023, 8 (02) :4645-4665

[17]

Miller K. S., 1993, INTRO FRACTIONAL CAL

[18]

Podlubny I, 1999, Fractional Differential Equations, DOI DOI 10.12691/AJMA-1-1-3

[19] Analysis of Existence and Stability Results for Impulsive Fractional Integro-Differential Equations Involving the Atangana-Baleanu-Caputo Derivative under Integral Boundary Conditions [J].

Reunsumrit, Jiraporn ;

Karthikeyann, Panjaiyan ;

Poornima, Sadhasivam ;

Karthikeyan, Kulandhaivel ;

Sitthiwirattham, Thanin .

MATHEMATICAL PROBLEMS IN ENGINEERING, 2022, 2022

[20] Analysis of a Fractional-Order Model for African Swine Fever with Effect of Limited Medical Resources [J].

Shi, Ruiqing ;

Li, Yang ;

Wang, Cuihong .

FRACTAL AND FRACTIONAL, 2023, 7 (06)

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