scholarly journals Existence and Uniqueness Theorems For Non- Linear Fractional Differential Equations

2006 ◽  
Vol 18 (2) ◽  
pp. 104-116
Author(s):  
Azhaar H. Sallo
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Theorems ◽  
Existence And Uniqueness Theorems ◽  
Non Linear ◽  
Fractional Differential ◽  
Linear Fractional Differential Equations

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.

scholarly journals Analysis of a System for Linear Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Fang Wang ◽  
Zhen-hai Liu ◽  
Ping Wang
Keyword(s):  
Differential Equations ◽  
Unique Solution ◽  
Fractional Differential Equations ◽  
Constant Coefficient ◽  
Existence And Uniqueness ◽  
Diagonal Matrix ◽  
Fractional Differential ◽  
Homogeneous Linear ◽  
Linear Fractional Differential Equations

The main purpose of this paper is to obtain the unique solution of the constant coefficient homogeneous linear fractional differential equationsDt0qX(t)=PX(t),X(a)=Band the constant coefficient nonhomogeneous linear fractional differential equationsDt0qX(t)=PX(t)+D,X(a)=BifPis a diagonal matrix andX(t)∈C1-q[t0,T]×C1-q[t0,T]×⋯×C1-q[t0,T]and prove the existence and uniqueness of these two kinds of equations for anyP∈L(Rm)andX(t)∈C1-q[t0,T]×C1-q[t0,T]×⋯×C1-q[t0,T]. Then we give two examples to demonstrate the main results.

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