scholarly journals Existence results for fractional neutral functional integro-differential evolution equations with infinite delay in Banach spaces

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Chokkalingam Ravichandran ◽  
Dumitru Baleanu
Keyword(s):  
Differential Evolution ◽  
Banach Spaces ◽  
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 The Impulsive Neutral Integro-Differential Equations with Infinite Delay and Non-Instantaneous Impulses

2018 ◽  
Vol 7 (4.10) ◽  
pp. 694
Author(s):  
V. Usha ◽  
M. Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Semigroup Theory ◽  
Existence Results ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Fixed Point Theorem

In this manuscript, we work to accomplish the Krasnoselskii's fixed point theorem to analyze the existence results for an impulsive neutral integro-differential equations  with infinite delay and non-instantaneous impulses in Banach spaces. By deploying the fixed point theorem with semigroup theory, we developed the coveted outcomes.   

scholarly journals On the Behaviour of Singular Semigroups in Intermediate and Interpolation Spaces and Its Applications to Maximal Regularity for Degenerate Integro-Differential Evolution Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-37 ◽  
Author(s):  
Alberto Favaron ◽  
Angelo Favini
Keyword(s):  
Differential Evolution ◽  
Banach Spaces ◽  
Wide Class ◽  
Evolution Equations ◽  
Maximal Regularity ◽  
Linear Operators ◽  
Interpolation Spaces ◽  
Power Type ◽  
Maximal Time

For those semigroups, which may have power type singularities and whose generators are abstract multivalued linear operators, we characterize the behaviour with respect to a certain set of intermediate and interpolation spaces. The obtained results are then applied to provide maximal time regularity for the solutions to a wide class of degenerate integro- and non-integro-differential evolution equations in Banach spaces.

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

scholarly journals Existence results for differential evolution equations with nonlocal conditions in Banach space

2018 ◽  
Vol 06 (02) ◽  
pp. 457-466
Author(s):  
Hedia Benaouda ◽  
Johnny Henderson ◽  
Berrabah Fatima Zohra
Keyword(s):  
Banach Space ◽  
Differential Evolution ◽  
Evolution Equations ◽  
Nonlocal Conditions ◽  
Existence Results

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.

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