STABILITY THEORY FOR MULTI-ORDER FRACTIONAL DIFFERENTIAL EQUATIONS

The theory of fractional differential equations has been recently developed and the existing fundamental results have been presented in a unified way in a research monograph [4]. This provides us with an advantage to understand and appreciate the intricacies involved so as to pave the way for further development of this important subject as an independent branch of nonlinear analysis. In a recent paper, [3] we have discussed the relation between the solutions of fractional differential equations and the solutions of ordinary differential equations. Since the properties of solutions of ODEs is relatively easier to investigate due to its well developed theory, the advantage of the relationship between the two systems is quite clear. In this paper, we shall consider multi-order fractional differential equations, develop needed mechanism of generalized spaces, utilize the method of vector Lyapunov functions and use the modified procedure discussed in [3] to study stability theory of multi-order fractional differential systems by relating them to the corresponding ordinary differential systems. We believe that the mechanism developed in this paper would be very useful to investigate further multi-order systems to obtain various other results.