On fractional differential equations with state-dependent delay via Kuratowski measure of noncompactness

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 451-460 ◽  
Author(s):  
Mohammed Belmekki ◽  
Kheira Mekhalfi
Keyword(s):  
Differential Equations ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Kuratowski Measure Of Noncompactness ◽  
State Dependent ◽  
State Dependent Delay ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Functional Differential

This paper is devoted to study the existence of mild solutions for semilinear functional differential equations with state-dependent delay involving the Riemann-Liouville fractional derivative in a Banach space and resolvent operator. The arguments are based upon M?nch?s fixed point theoremand the technique of measure of noncompactness.

Stability results for fractional differential equations with state-dependent delay and not instantaneous impulses

2017 ◽  
Vol 67 (4) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Darboux Problem ◽  
State Dependent ◽  
State Dependent Delay ◽  
Fractional Differential ◽  
Functional Differential ◽  
Ulam’S Type Stability ◽  
Stability Results ◽  
Stability Concepts

AbstractIn this paper, we shall present some uniqueness and Ulam’s type stability concepts for the Darboux problem of partial functional differential equations with not instantaneous impulses and state-dependent delay in Banach spaces. Some examples are also provided to illustrate our results.

scholarly journals Approximate Controllability for Functional Equations with Riemann-Liouville Derivative by Iterative and Approximate Method

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Badawi Hamza Elbadawi Ibrahim ◽  
Zhenbin Fan ◽  
Gang Li
Keyword(s):  
Differential Equations ◽  
Approximate Method ◽  
Approximate Controllability ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Liouville Derivative ◽  
Liouville Fractional Derivative ◽  
Functional Control ◽  
Functional Differential

We discuss the functional control systems governed by differential equations with Riemann-Liouville fractional derivative in general Banach spaces in the present paper. First we derive the uniqueness and existence of mild solutions for functional differential equations by the approach of fixed point and fractional resolvent under more general settings. Then we present new sufficient conditions for approximate controllability of functional control system by means of the iterative and approximate method. Our results unify and generalize some previous works on this topic.

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