Mathematical Innovation Unravelling Physical World Complexities: A Comprehensive Study of Fuzzy Metrics and Fixed-Point Theory in Boundary Value Problems

Abstract

Often there arises a problematic situation in the realistic world scenario where affirmations cannot be addressed in terms of exact truthfulness or falsity. Such troublesome challenges are to be addressed by reckoning the flexible membership, the values of which lies between total falsity (0) and total truthfulness (1). The foundation of fuzzy theory comprises of the grade-ship function which is also recognised as membership function. On the flip side, the notion of metric (distance) has a wide range of applications in practical scenarios, which indeed after getting fuzzified under the title of fuzzy metric offers a strong mathematical perspective enabling the feasibility of the solutions of various complex problems. The main objective of this project is to employ fixed-point theory in fuzzy metric and related setup(s) to provide the solution of the boundary value problem (BVP) dealing with the physical world problem(s). This research presents novel mathematical formulations that bridge theoretical fuzzy mathematics with practical engineering applications, demonstrating significant improvements in solving complex boundary value problems through advanced fixed-point techniques.