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This book explores the latest advancements in applied mathematical analysis, presenting cutting-edge research across a diverse array of topics, from arithmetic functions linked to non-trivial zeta zeros to innovative methods for solving ordinary differential equations using neural networks. Readers will encounter an array of subjects, including the intricacies of functional equations in fuzzy Banach spaces, vector inequalities in Hilbert spaces, and the complexities of fluid-structure interaction methods for the Navier–Stokes equations. The volume also delves into the characterization of coercivity in preordered pseudometric spaces and the localization of fractional spectra for operators in Hilbert spaces. Each chapter, contributed by leading experts, provides a deep dive into these complex topics, offering both theoretical insights and practical applications. This book is an invaluable resource for researchers, scholars, and practitioners in the field of mathematical analysis and its applications. Whether you're a mathematician, physicist, or engineer, Trends in Applied Mathematical Analysis will enhance your understanding and inspire new approaches to solving interdisciplinary problems.