Solution of nonlinear difference equations with invers q-difference operator

In this study, information is given about the q-difference equation and the q-operator, which form the basis of Q-analysis, based on ordinary difference, and after the definitions and applications, D_q and D_(q^(-1) ) operators are introduced. In the following sections of the study, the formation process of the q-difference equation, whose solution family is given depending on an arbitrary constant, is explained. The similarities and differences between classical differential equations and q-difference equations at some points are shown, and the existence of q-derivative in definition intervals where there is no derivative in the solution families, and in some cases the situations where the derivative and q-derivative overlap are shown with examples. Within the scope of difference equations, although it is known that it is not possible to reach general solutions of non-linear type equations or requires long efforts, non-linear difference equations are used in many fields of engineering and natural sciences. Therefore, in this study, methods of finding solution families of nonlinear q-difference equations, which are used in modeling many problems, with the inverse q-difference operator are explained with theories and examples. Solution families of nonlinear q-difference equations were found by making them linear, if appropriate, or by transforming them into the forms given in the study, depending on whether they are homogeneous or non-homogeneous.