A Comprehensive Study on System of q-Difference Equation

＂A Comprehensive Study on System of Difference Equation,＂ focuses on the mathematical study of q-difference equations. Here are the main aspects of the thesis:1. Definition and Framework: The thesis begins by defining q-difference equations and establishing a theoretical framework to analyze their properties. This includes an exploration of various types of difference equations and their significance in mathematics.2. Existence and Uniqueness of Solutions: A significant portion of the research is dedicated to investigating the existence and uniqueness of solutions to these equations. We employs methods such as Jackson integrals to demonstrate these properties and support his findings through specific examples, including the second-order Cauchy problem.3. Historical Context: The thesis places -difference equations within a historical context, reviewing previous research and contributions by notable mathematicians. This historical perspective helps to frame our Luqwork as an extension and adaptation of established theories in the field.