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Study of Non-Linear Impulsive Neutral Fuzzy Delay Differential Equations with Non-Local Conditions

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  • Tharmalingam Gunasekar

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India
    School of Artificial Intelligence & Data Science, Indian Institute of Technology (IIT), Jodhpur 600036, India)

  • Jothivelu Thiravidarani

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India)

  • Miroslav Mahdal

    (Department of Control Systems and Instrumentation, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 17. Listopadu 2172/15, 70800 Ostrava, Czech Republic)

  • Prabakaran Raghavendran

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India)

  • Arikrishnan Venkatesan

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India)

  • Muniyandy Elangovan

    (Department of Biosciences, Saveetha School of Engineering, Saveetha Nagar, Thandalam 602105, India
    Department of R&D, Bond Marine Consultancy, London EC1V2NX, UK)

Abstract

This manuscript aims to investigate the existence and uniqueness of fuzzy mild solutions for non-local impulsive neutral functional differential equations of both first and second order, incorporating finite delay. Furthermore, the study explores the properties of fuzzy set-valued mappings of a real variable, where these mappings exhibit characteristics such as normality, convexity, upper semi-continuity, and compact support. The application of the Banach fixed-point theorem is employed to derive the results. The research extensively employs fundamental concepts from fuzzy set theory, functional analysis, and the Hausdorff metric. Additionally, an illustrative example is provided to exemplify the practical implementation of the proposed concept.

Suggested Citation

  • Tharmalingam Gunasekar & Jothivelu Thiravidarani & Miroslav Mahdal & Prabakaran Raghavendran & Arikrishnan Venkatesan & Muniyandy Elangovan, 2023. "Study of Non-Linear Impulsive Neutral Fuzzy Delay Differential Equations with Non-Local Conditions," Mathematics, MDPI, vol. 11(17), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3734-:d:1229219
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    References listed on IDEAS

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    1. Xiao, Yiyong & Zhang, Yue & Kaku, Ikou & Kang, Rui & Pan, Xing, 2021. "Electric vehicle routing problem: A systematic review and a new comprehensive model with nonlinear energy recharging and consumption," Renewable and Sustainable Energy Reviews, Elsevier, vol. 151(C).
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