Functional analysis with fractional operators: properties and applications in metric spaces

Abstract

Functional analysis has witnessed significant advancements with the introduction of fractional operators, which extend the scope of fractional calculus to functional spaces. These operators provide a powerful framework for analyzing complex functions in metric spaces, enabling the study of nonlocal and non-smooth phenomena. In this paper, we delve into functional analysis with conformable fractional operators, exploring their properties and applications in metric spaces. We establish the theoretical foundations, discussing concepts from functional analysis and fractional calculus, and investigate the properties of conformable fractional operators, such as differentiability, boundedness, and compactness. Furthermore, we showcase the wide range of applications that arise from the utilization of these operators, spanning physics, engineering, biology, and data science. Through the analysis of real-world examples and numerical simulations, we demonstrate the practical utility and effectiveness of conformable fractional operators in capturing intricate dynamics. Overall, this paper provides a comprehensive overview of functional analysis with fractional operators, highlighting their significance in understanding and addressing complex phenomena in metric spaces.