In this paper we study the existence and continuation of solution to the general fractional differential equation (FDE) with Riemann-Liouville derivative. If no confusion appears, we call FDE for brevity. We firstly establish a new local existence theorem. Then, we derive the continuation theorems for the general FDE, which can be regarded as a generalization of the continuation theorems of the ordinary differential equation (ODE). Such continuation theorems for FDE which are first obtained are different from those for the classical ODE. With the help of continuation theorems derived in this paper, several global existence results for FDE are constructed. Some illustrative examples are also given to verify the theoretical results.
|Journal||International Journal of Bifurcation and Chaos in Applied Sciences and Engineering|
|State||Published - Apr 2012|
- Fractional differential equations
- Riemann-Liouville derivative
- continuation theorem
- global solution
- local existence