Some analytical solution methods and applications for Volterra integral equations

This thesis aims to examine the definition, types, and classification of integral equations, converting different equations with constant and variable coefficients into integral equations, and solving them using various methods to evaluate the results. Integral equations have an important role in mathematical modeling and analysis of physical systems. For this reason, the results obtained from its widespread use in technology and especially in many engineering fields make significant contributions to science and engineering. This study addresses the general structure of integral equations, various solution methods, and their applications. The first part of the study provides information about the history of integral equations and the work done up to the present day. The second part presents an overview of the basic concepts of integral equations. The third part classifies and explains these equations according to their different characteristics. In the fourth part, the relationship between differential equations and integral equations is explained, along with the methods of converting them into each other. The fifth part discusses the solution methods of Volterra integral equations and provides applications of these methods.