Controllability of impulsive stochastic partial integrodifferential equation with noncompact semigroups

2019 ◽  
Vol 39 (2) ◽  
pp. 159
Author(s):  
Ibrahim Mahamat Barka ◽  
Mamadou Abdoul Diop ◽  
Khalil Ezzinbi ◽  
Mahamat Hassan Mahamat Hamit
Keyword(s):  
Integrodifferential Equation ◽  
Partial Integrodifferential Equation

scholarly journals Asymptotic Behavior of Solutions to Abstract Stochastic Fractional Partial Integrodifferential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhi-Han Zhao ◽  
Yong-Kui Chang ◽  
Juan J. Nieto
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Integrodifferential Equation ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
Integrodifferential Equations ◽  
Linear Operators ◽  
Asymptotic Behavior Of Solutions ◽  
Almost Automorphic ◽  
Partial Integrodifferential Equation

The existence of asymptotically almost automorphic mild solutions to an abstract stochastic fractional partial integrodifferential equation is considered. The main tools are some suitable composition results for asymptotically almost automorphic processes, the theory of sectorial linear operators, and classical fixed point theorems. An example is also given to illustrate the main theorems.

scholarly journals On Some Nonlinear Integrodifferential Inequalities for Functions of Independent Variables

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
Hassane Khellaf ◽  
Mohamed El-Hadi Smakdji
Keyword(s):  
Integrodifferential Equation ◽  
Qualitative Theory ◽  
Integral Inequalities ◽  
Independent Variables ◽  
Partial Integrodifferential Equation ◽  
New Inequalities

The object of this paper is to establish some nonlinear integrodifferential integral inequalities in independent variables. These new inequalities represent a generalization of the results obtained by Pachpatte in the case of a function with one and two variables. Our results can be used as tools in the qualitative theory of a certain class of partial integrodifferential equation.

scholarly journals Chebyshev Collocation Method for Parabolic Partial Integrodifferential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
M. Sameeh ◽  
A. Elsaid
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Error Estimate ◽  
Collocation Method ◽  
Integrodifferential Equation ◽  
Chebyshev Polynomials ◽  
Difference Method ◽  
A Priori ◽  
Chebyshev Collocation Method ◽  
Partial Integrodifferential Equation

An efficient technique for solving parabolic partial integrodifferential equation is presented. This technique is based on Chebyshev polynomials and finite difference method.A priorierror estimate for the proposed technique is deduced. Some examples are presented to illustrate the validity and efficiency of the presented method.

scholarly journals Existence of Solutions of a Partial Integrodifferential Equation with Thermostat and Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Carlo Bianca ◽  
Luca Guerrini ◽  
Annie Lemarchand
Keyword(s):  
Cauchy Problem ◽  
Time Delay ◽  
Integrodifferential Equation ◽  
Mathematical Analysis ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Kinetic Equations ◽  
Successive Approximations ◽  
Partial Integrodifferential Equation

This paper deals with the mathematical analysis of a retarded partial integrodifferential equation that belongs to the class of thermostatted kinetic equations with time delay. Specifically, the paper is devoted to the proof of the existence and uniqueness of mild solutions of the related Cauchy problem. The main result is obtained by employing integration along the characteristic curves and successive approximations sequence arguments. Applications and perspective are also discussed within the paper.

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

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