Existence and uniqueness of solutions in mathematical equations: exploring novel approaches in a metric space

Abstract

This paper gives a thorough study of the existence and uniqueness of solutions for a large variety of mathematical problems in a metric space. We lay the theoretical groundwork and develop the computational methods required for resolving complicated issues by utilizing unique strategies based on ordinary, partial, and fractional differential equations. We illustrate the efficiency and dependability of these approaches in delivering solid answers through in-depth research, numerical simulations, and real-world applications. The variety and applicability of the suggested solutions are demonstrated by various examples and case studies. Our discoveries expand computational and scientific modeling methods, enabling researchers to take on difficult challenges in a variety of fields.