New results concerning to approximate controllability of fractional integro‐differential evolution equations of order 1 <  r  < 2

2020 ◽  
Author(s):  
M. Mohan Raja ◽  
V. Vijayakumar
Keyword(s):  
Differential Evolution ◽  
Approximate Controllability ◽  
Evolution Equations

scholarly journals Approximate controllability of second-order nonlocal impulsive partial functional integro-differential evolution systems in Banach spaces

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5887-5912 ◽  
Author(s):  
Mahalingam Nagaraj ◽  
Velusamy Kavitha ◽  
Dumitru Baleanu ◽  
Mani Arjunan
Keyword(s):  
Differential Evolution ◽  
Banach Spaces ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Nonlinear Alternative ◽  
Banach Contraction

This manuscript is involved with a class of second-order impulsive partial functional integro-differential evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions ensuring the existence and approximate controllability of mild solutions are established. Theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem are employed for achieving the required results. An example is analyzed to illustrate the effectiveness of the outcome.

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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