Existence and uniqueness of solutions to impulsive fractional differential equations via the deformable derivative

2021 ◽  
pp. 1-12
Author(s):  
Mesfin Etefa ◽  
Gaston M. N'Guérékata ◽  
Mouffak Benchohra
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

scholarly journals Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Lakshman Mahto ◽  
Syed Abbas ◽  
Angelo Favini
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Logistic Model ◽  
Fixed Point Method ◽  
Uniqueness Of Solutions ◽  
Fractional Order Differential Equations ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We use Sadovskii's fixed point method to investigate the existence and uniqueness of solutions of Caputo impulsive fractional differential equations of order with one example of impulsive logistic model and few other examples as well. We also discuss Caputo impulsive fractional differential equations with finite delay. The results proven are new and compliment the existing one.

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 Complex Transforms for Systems of Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

We provide a complex transform that maps the complex fractional differential equation into a system of fractional differential equations. The homogeneous and nonhomogeneous cases for equivalence equations are discussed and also nonequivalence equations are studied. Moreover, the existence and uniqueness of solutions are established and applications are illustrated.

Sign in / Sign up

Export Citation Format

Share Document