scholarly journals Existence and uniqueness theorems for sequential linear conformable fractional differential equations

2016 ◽  
Vol 17 (1) ◽  
pp. 267 ◽  
Author(s):  
Ahmet Gökdogan ◽  
Emrah Ünal ◽  
Ercan Celik
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Theorems ◽  
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.

On Abstract Fractional Order Telegraph Equation

2010 ◽  
Vol 5 (2) ◽  
Author(s):  
Mohamed A. E. Herzallah ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Telegraph Equation ◽  
Uniqueness Theorems ◽  
Science And Engineering ◽  
New Model ◽  
Fractional Differential

During the last decades, there has been a great deal of interest in fractional differential equations and their applications in various fields of science and engineering. In this paper, we give a new model of the abstract fractional order telegraph equation and we study the existence and uniqueness theorems of the strong and mild solutions as well as the continuation of this solution. To illustrate the obtained results, two examples were analyzed in detail.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

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