This book presents the essential role of mathematical modelling and computational methods in representing physical phenomena mathematically, focusing on the significance of the I-function. Serving as a generalized form of special functions, particularly generalised hypergeometric functions, the I-function emerges from solving dual integral equations, prevalent in scenarios such as mixed boundary problems in potential theory, energy diffusion, and population dynamics. Offers the most recent developments on I-function and their application in mathematical modelling and possible applications to some other research areas Expands the area of special functions that have been developed and applied in a variety of fields, such as combinatory, astronomy, applied mathematics, physics, and engineering Highlights the importance of fundamental results and techniques based on the theory of complex analysis and emphasizes articles devoted to the mathematical aspect and applications Shows the importance of fundamental results and techniques derived from the theory of complex analysis, laying the groundwork for further exploration and potential applications of the I-function in solving complex problems Discusses dual integral equations solving and its crucial role in various physical phenomena, such as potential theory and population dynamics Expanding the field of special functions, I-function and Its Applications serves as a platform for recent theories and applications, offering students, researchers, and scholars of Mathematics insight into advanced mathematical techniques and their practical implications across various fields.