Existence Results for Fractional Order Semilinear Integro-Differential Evolution Equations with Infinite Delay

2010 ◽  
Vol 67 (1) ◽  
pp. 33-49 ◽  
Author(s):  
Yong Ren ◽  
Yan Qin ◽  
R. Sakthivel
Keyword(s):  
Differential Evolution ◽  
Fractional Order ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Existence Results

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.

scholarly journals Existence Results for Semilinear Differential Evolution Equations with Impulses and Delay

Cubo (Temuco) ◽  
2010 ◽  
Vol 12 (2) ◽  
pp. 1-17 ◽  
Author(s):  
Nadjet Abada ◽  
Mouffak Benchohra ◽  
Hadda Hammouche
Keyword(s):  
Differential Evolution ◽  
Evolution Equations ◽  
Existence Results

Existence, uniqueness and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
JinRong Wang ◽  
Chun Zhu ◽  
Michal Fečkan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Fractional Order ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Limit Property ◽  
Type Integral

AbstractIn this paper, we apply certain measure of noncompactness and fixed point theorem of Darbo type to derive the existence and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order with three parameters. Moreover, we also present the uniqueness and another existence results of the solutions to the above equations. Finally, two examples are given to illustrate the obtained results.

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