Non-uniqueness of solution for initial value problem of impulsive Caputo-Katugampola fractional differential equations

2020 ◽  
Vol 10 (3) ◽  
pp. 183
Author(s):  
Xianmin Zhang
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Initial Value Problem ◽  
Uniqueness Of Solution ◽  
Initial Value ◽  
Fractional Differential

scholarly journals Initial Value Problem For Nonlinear Fractional Differential Equations With ψ-Caputo Derivative Via Monotone Iterative Technique

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 57 ◽  
Author(s):  
Choukri Derbazi ◽  
Zidane Baitiche ◽  
Mouffak Benchohra ◽  
Alberto Cabada
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Initial Value Problem ◽  
Caputo Derivative ◽  
Monotone Iterative Technique ◽  
Extremal Solutions ◽  
Iterative Technique ◽  
Initial Value ◽  
Monotone Iterative ◽  
Fractional Differential

In this article, we discuss the existence and uniqueness of extremal solutions for nonlinear initial value problems of fractional differential equations involving the ψ -Caputo derivative. Moreover, some uniqueness results are obtained. Our results rely on the standard tools of functional analysis. More precisely we apply the monotone iterative technique combined with the method of upper and lower solutions to establish sufficient conditions for existence as well as the uniqueness of extremal solutions to the initial value problem. An illustrative example is presented to point out the applicability of our main results.

On coupled system of nonlinear Ψ-Hilfer hybrid fractional differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ashwini D. Mali ◽  
Kishor D. Kucche ◽  
José Vanterler da Costa Sousa
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Initial Value Problem ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Coupled System ◽  
Initial Value ◽  
Fractional Differential

Abstract This paper is dedicated to investigating the existence of solutions to the initial value problem (IVP) for a coupled system of Ψ-Hilfer hybrid fractional differential equations (FDEs) and boundary value problem (BVP) for a coupled system of Ψ-Hilfer hybrid FDEs. Analysis of the current paper depends on the two fixed point theorems involving three operators characterized on Banach algebra. In the view of an application, we provided useful examples to exhibit the effectiveness of our achieved results.

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