Mild Solution of Second-Order Impulsive Integro-Differential Evolution Equations of Volterra Type in Banach Spaces

2020 ◽  
Vol 19 (1) ◽  
Author(s):  
Xinan Hao ◽  
Lishan Liu
Keyword(s):  
Differential Evolution ◽  
Banach Spaces ◽  
Mild Solution ◽  
Evolution Equations ◽  
Second Order ◽  
Volterra Type

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.

scholarly journals Existence and optimal controls for nonlocal fractional evolution equations of order (1,2) in Banach spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Denghao Pang ◽  
Wei Jiang ◽  
Azmat Ullah Khan Niazi ◽  
Jiale Sheng
Keyword(s):  
Banach Spaces ◽  
Mild Solution ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Well Posedness ◽  
Optimal Controls ◽  
Lagrange Problem ◽  
Fractional Differential ◽  
Fractional Evolution Systems ◽  
Definition Of

AbstractIn this paper, we mainly investigate the existence, continuous dependence, and the optimal control for nonlocal fractional differential evolution equations of order (1,2) in Banach spaces. We define a competent definition of a mild solution. On this basis, we verify the well-posedness of the mild solution. Meanwhile, with a construction of Lagrange problem, we elaborate the existence of optimal pairs of the fractional evolution systems. The main tools are the fractional calculus, cosine family, multivalued analysis, measure of noncompactness method, and fixed point theorem. Finally, an example is propounded to illustrate the validity of our main results.

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.

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