Results on the existence of Hilfer fractional neutral evolution equations with infinite delay via measures of noncompactness

2020 ◽  
Vol 44 (2) ◽  
pp. 1438-1455 ◽  
Author(s):  
K. Kavitha ◽  
V. Vijayakumar ◽  
R. Udhayakumar ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Evolution Equations ◽  
Infinite Delay ◽  
Neutral Evolution ◽  
Measures Of Noncompactness ◽  
Fractional Neutral Evolution Equations

scholarly journals Approximate Controllability of Fractional Neutral Evolution Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
N. I. Mahmudov
Keyword(s):  
Fixed Point ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Neutral Evolution ◽  
Differential Systems ◽  
Neutral Differential Equations ◽  
Approximately Controllable ◽  
Fractional Neutral Evolution Equations

We discuss the approximate controllability of semilinear fractional neutral differential systems with infinite delay under the assumptions that the corresponding linear system is approximately controllable. Using Krasnoselkii's fixed-point theorem, fractional calculus, and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional neutral differential equations with infinite delay are formulated and proved. The results of the paper are generalization and continuation of the recent results on this issue.

scholarly journals On the Aronszajn property for fractional neutral evolution equations with infinite delay on half-line

2020 ◽  
Vol 21 (2) ◽  
pp. 767-790
Author(s):  
Nguyen Ngoc Trong ◽  
◽  
Le Xuan Truong ◽  
Nguyen Thanh Tung ◽  
◽  
...  
Keyword(s):  
Evolution Equations ◽  
Infinite Delay ◽  
Neutral Evolution ◽  
Half Line ◽  
Fractional Neutral Evolution Equations

scholarly journals Existence of Solutions for Fractional Evolution Equations with Infinite Delay and Almost Sectorial Operator

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Shanshan Li ◽  
Shuqin Zhang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Sectorial Operator ◽  
Analytic Semigroups ◽  
Measures Of Noncompactness ◽  
Fractional Evolution Equations

This paper discusses a class of semilinear fractional evolution equations with infinite delay and almost sectorial operator on infinite interval in Banach space. By using the properties of analytic semigroups and Schauder’s fixed-point theorem, this paper obtains the existence of mild solutions of the fractional evolution equation. Moreover, this paper also discusses the existence of mild solution when the analytic semigroup lacks compactness by Kuratowski measures of noncompactness and Darbo–Sadovskii fixed-point theorem.

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Shengli Xie
Keyword(s):  
Differential Equations ◽  
Differential Evolution ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Existence Results ◽  
Order Case

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.

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