TY - JOUR
T1 - Existence and continuation theorems of riemann-liouville type fractional differential equations
AU - Kou, Chunhai
AU - Zhou, Huacheng
AU - Li, Changpin
N1 - Funding Information:
The present job was in part financially supported by the National Natural Science Foundation of China (Nos. 10701023, 10872119 and 10971221), Shanghai Leading Academic Discipline (No. S30104), and Shanghai Natural Science Foundation (No. 10ZR1400100).
PY - 2012/4
Y1 - 2012/4
N2 - 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.
AB - 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.
KW - Fractional differential equations
KW - Riemann-Liouville derivative
KW - continuation theorem
KW - global solution
KW - local existence
UR - http://www.scopus.com/inward/record.url?scp=84861211229&partnerID=8YFLogxK
U2 - 10.1142/S0218127412500770
DO - 10.1142/S0218127412500770
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AN - SCOPUS:84861211229
SN - 0218-1274
VL - 22
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
IS - 4
M1 - 1250077
ER -