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Article | Open Access

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

Nagalakshmi Soma1, Grande Suresh Kumar1( ), Ravi Prakash Agarwal2, Chao Wang3, Madhunapantula Surya Narayana Murty4
Department of Mathematics, Koneru Lakshmaiah Education Foundation, Guntur 522302, India
Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USA
Department of Mathematics, Yunnan University, Kunming 650091, China
Department of Mathematics, Acharya Nagarjuna University, Guntur 521201, India
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Abstract

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.

Keywords

granular differentiabilityhorizontal membership functioncontraction mappingfuzzy boundary value problem

References

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Fuzzy Information and Engineering
Volume 15 Issue 3,
September 2023
Pages 291-312
DOI: 10.26599/FIE.2023.9270021

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Cite this article:
Soma N, Suresh Kumar G, Agarwal RP, et al. Existence and Uniqueness of Solutions for Fuzzy Boundary Value Problems Under Granular Differentiability. Fuzzy Information and Engineering, 2023, 15(3): 291-312. https://doi.org/10.26599/FIE.2023.9270021

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Received: 28 May 2023
Revised: 25 July 2023
Accepted: 15 August 2023
Published: 01 September 2023
© The Author(s) 2023. Published by Tsinghua University Press.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).