EXISTENCE AND UNIQUENESS THEOREMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

2000 ◽  
Vol 33 (3) ◽  
Author(s):  
A. A. Kilbas ◽  
B. Bonilla ◽  
J . J. Trujillo
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Theorems ◽  
Nonlinear Fractional Differential Equations ◽  
Existence And Uniqueness Theorems ◽  
Fractional Differential

scholarly journals The Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for CFR Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Xia Wang ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Type Inequality ◽  
Uniqueness Theorems ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Maximum Value ◽  
Fractional Differential ◽  
Lyapunov Type Inequality

In this paper, we research CFR fractional differential equations with the derivative of order 3<α<4. We prove existence and uniqueness theorems for CFR-type initial value problem. By Green’s function and its corresponding maximum value, we obtain the Lyapunov-type inequality of corresponding equations. As for application, we study the eigenvalue problem in the sense of CFR.

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