Existence and Uniqueness of Solutions for Fuzzy Boundary Value Problems Under Granular Differentiability

被引：1

作者：

Soma, Nagalakshmi ^{[1
]}

Kumar, Grande Suresh ^{[1
]}

Agarwal, Ravi Prakash ^{[2
]}

Wang, Chao ^{[3
]}

Murty, Madhunapantula Surya Narayana ^{[4
]}

机构：

[1] Koneru Lakshmaiah Educ Fdn, Dept Math, Guntur 522302, India

[2] Texas A&M Univ, Dept Math, Kingsville, TX 78363 USA

[3] Yunnan Univ, Dept Math, Kunming 650091, Peoples R China

[4] Acharya Nagarjuna Univ, Dept Math, Guntur 521201, India

来源：

FUZZY INFORMATION AND ENGINEERING | 2023年 / 15卷 / 03期

关键词：

granular differentiability; horizontal membership function; contraction mapping; fuzzy boundary value problem; EQUATIONS;

D O I：

10.26599/FIE.2023.9270021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper considers fuzzy boundary value problems associated with second-order fuzzy differential equations under granular differentiability. Using a horizontal membership function, we present the notion of second-order granular differentiability for fuzzy functions. Using the granular differentiability concept, we interpret two kinds of two-point boundary value problems for second-order fuzzy differential equations. Sufficient conditions are established for the existence and uniqueness of solutions to these fuzzy boundary value problems. An algorithm is presented for solving non-linear fuzzy boundary value problems under granular differentiability. We provide one example and two engineering applications to demonstrate the algorithm's effectiveness and results.

引用

页码：291 / 312

页数：22

共 50 条

[41] Shape differentiability of solutions of boundary value problems and approximate solutions
Belov, SA
DIFFERENTIAL EQUATIONS, 2002, 38 (01) : 67 - 74
[42] Differentiability of solutions of boundary value problems with respect to data
Vidossich, G
JOURNAL OF DIFFERENTIAL EQUATIONS, 2001, 172 (01) : 29 - 41
[43] EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A PERIODIC BOUNDARY VALUE PROBLEM
Amini-Harandi, A.
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2013, 39 (01): : 165 - 173
[44] Uniqueness and existence for perturbed focal boundary value problems
Ehme, J
APPLIED MATHEMATICS LETTERS, 2005, 18 (08) : 875 - 879
[45] EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A NONLINEAR BOUNDARY VALUE PROBLEM
WALTMAN, P
JOURNAL OF MATHEMATICS AND MECHANICS, 1968, 18 (06): : 585 - &
[46] UNIQUENESS OF SOLUTIONS FOR DISCRETE BOUNDARY VALUE PROBLEMS
Galewski, Marek
DYNAMIC SYSTEMS AND APPLICATIONS, 2013, 22 (01): : 105 - 113
[47] Existence-uniqueness of solutions for fuzzy nabla initial value problems on time scales
Leelavathi, R.
Kumar, G. Suresh
Murty, M. S. N.
Rao, R. V. N. Srinivasa
ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (1)
[48] Existence-uniqueness of solutions for fuzzy nabla initial value problems on time scales
R. Leelavathi
G. Suresh Kumar
M. S. N. Murty
R. V. N. Srinivasa Rao
Advances in Difference Equations, 2019
[49] UNIQUENESS OF SOLUTIONS FOR CERTAIN BOUNDARY VALUE PROBLEMS
JUBERG, RK
SIAM REVIEW, 1970, 12 (03) : 461 - &
[50] Existence and uniqueness of solutions for singular higher order continuous and discrete boundary value problems
Yuan, Chengjun
Jiang, Daqing
Zhang, You
BOUNDARY VALUE PROBLEMS, 2008, 2008 (1)

← 1 2 3 4 5 →