Research Specifications

preface The ordinary differential and integral calculus (classic calculus), which was introduced in the late 17th century by Isaac Newton from England and Gottfried Leibniz from Germany, was able to model many natural phenomena, physics and engineering problems with the help of differential equations. This calculus, which we refer to as continuous additive calculus in this book, could only model problems and phenomena that change in a continuous environment with continuous variables. This calculus is also used for discrete environments and discrete variables by approximating and accepting the error of the method in modeling these problems. The mathematical models for discrete systems with discrete variables are difference equations, which is actually the discrete analogy of differential equations. Differential equations have made a lot of progress both in terms of the theory related to the existence and uniqueness of solutions and the quality of the solutions and also in terms of solving methods within the last three hundred years. While the progress of difference equations has not been like this. Especially, the investigation and solution of nonlinear difference equations is lagging behind both in terms of theory and in terms of solving techniques. For this purpose, calculus and analysis that can develop and improve the methods of solving initial value and boundary value problems including such equations is one of the necessities of new mathematics. In order to achieve this goal, many mathematicians have conducted studies and researches in recent years, which have come out in the form of books, articles, and doctoral theses, which are briefly mentioned in the historical background section. In continuation of the done work and after years of teaching and research in the field of new calculus, which are known as non-Newtonian calculus, we were able to give the present book with the title of discrete and continuous multiplicative calculus and their applications. The b