Study of Non-Linear Impulsive Neutral Fuzzy Delay Differential Equations with Non-Local Conditions
Tharmalingam Gunasekar,
Jothivelu Thiravidarani,
Miroslav Mahdal,
Prabakaran Raghavendran,
Arikrishnan Venkatesan,
Muniyandy Elangovan
Affiliations
Tharmalingam Gunasekar
Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, 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
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.
