Stability Analysis Of Fractional Differential Systems

This dissertation includes five chapters, and the body of the dissertation can be mainly divided into three parts:the initialization of the fractional calculus (the fractional integral and the fractional derivatives), the stability analysis of fractional differential sys-tems with the same order and the multi-order fractional differential systems.The first chapter briefly introduces the development of fractional calculus and the background of stability of fractional differential systems.The second chapter studies the Lorenzo-Hartley (LH) general initialization issues in the sense of Riemann-Liouville derivative and Caputo derivative, and compares the uninitialized Riemann-Liouville derivative with the LH initialized derivative in the sense of Riemann-Liouville from three angles.In chapterâ…¢, the stability of the same order linear fractional differential systems and their perturbed systems is studied, and the stability results for the same order linear fractional differential systems and the corresponding perturbed systems with Riemann-Liouville derivative and/or Caputo derivative are also given.Chapterâ…£analyzes the stability of the same order nonlinear fractional differential systems with Caputo derivative by using a Lyapunov-like function and the comparison principle, and derives some sufficient conditions on asymptotical stability and/or stabil-ity.In the last chapter, with the relationships between Caputo derivative and General-ized fractional derivative, we change the multi-order fractional differential system whose fractional order is rational into a much higher-dimensional fractional differential system with the same order lying in (0,1). Based on the equivalence results, the stability analysis of any multi-rational-order fractional differential system with Caputo derivative is given. Meanwhile, the equivalence and stability analysis of multi-rational-order fractional dif-ferential system with Riemann-Liouville derivative with the homogeneous initial value conditions are also provided, and a sufficient condition on stability is established.