Kesirli mertebeden lineer olmayan denklemlerin stabilizesi için lyapunov metodu

This thesis is divided into four chapters. The first chapter discusses the motivation for the thesis. It provides some basic information about nonlinear fractional derivatives, Riemann-Liouville derivative, and Caputo derivative. The second chapter provides important definitions and results to create an interesting background for all the new findings and their applications in numerical examples. In chapter three, the globally stable nonlinear system with partial Riemann-Liouville derivatives and Caputo derivatives is also introduced with many types of feedback controls, such as the feedback invariance problem and supported by many examples. In chapter four, the stability by using the direct method for some Lyapunov functions was applied to the system of fractional-differential- integral Riemann- Liouville type. The results supported by many examples explain details of the role of the Lyapunov-function for achieved stability, exponentially stable of composite fractional Riemann-Liouville differential-integral system.