scholarly journals Fractional nonlocal integrodifferential equations of mixed type with time-varying generating operators and optimal control

2010 ◽  
Vol 30 (2) ◽  
pp. 217 ◽  
Author(s):  
JinRong Wang ◽  
W. Wei ◽  
YanLong Yang
Keyword(s):  
Optimal Control ◽  
Mixed Type ◽  
Integrodifferential Equations ◽  
Time Varying ◽  
Equations Of Mixed Type ◽  
Generating Operators

scholarly journals Second-Order Nonlinear Impulsive Integro-Differential Equations of Mixed Type and Optimal Controls in Fractional Power Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-16
Author(s):  
Y. Peng
Keyword(s):  
Differential Equations ◽  
Principal Part ◽  
Mixed Type ◽  
Fractional Power ◽  
Second Order ◽  
Optimal Controls ◽  
Time Varying ◽  
Equations Of Mixed Type ◽  
Lagrange Problem ◽  
Generating Operators

A class of second-order nonlinear impulsive integro-differential equations of mixed type whose principal part is given by time-varying generating operators in fractional power spaces is considered. We introduce the reasonable PC-α-mild solution of second-order nonlinear impulsive integro-differential equations of mixed type and prove its existence. The existence of optimal controls for a Lagrange problem of systems governed by second-order nonlinear impulsive integro-equations of mixed type is also presented. An example is given for demonstration.

scholarly journals Periodic Solutions of Semilinear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
JinRong Wang ◽  
X. Xiang ◽  
W. Wei
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Mixed Type ◽  
Evolution Operator ◽  
Mild Solutions ◽  
Integral Operators ◽  
Periodic Systems ◽  
Time Varying ◽  
Type Integral ◽  
Generating Operators

A class of semilinear impulsive periodic systems with time-varying generating operators on Banach space is considered. Using impulsive periodic evolution operator given by us, theT0-periodicPC-mild solution is introduced and suitablePoincaréoperator is constructed. Showing the compactness ofPoincaréoperator and using a new generalized Gronwall inequality with mixed type integral operators given by us, we utilize Leray-Schauder fixed point theorem to prove the existence ofT0-periodicPC-mild solutions. Our method is an innovation and it is much different from methods of other papers. At last, an example is given for demonstration.

scholarly journals Solutions of nonlinear integrodifferential equations of mixed type in Banach spaces

1989 ◽  
Vol 2 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Mixed Type ◽  
Existence Of Solutions ◽  
Degree Theory ◽  
Monotone Iterative Technique ◽  
Integrodifferential Equations ◽  
Topological Degree Theory ◽  
Initial Value ◽  
Monotone Iterative ◽  
Equations Of Mixed Type ◽  
Minimal And Maximal Solutions

In this paper, the author combines the topological degree theory and the monotone iterative technique to investigate the existence of solutions and also minimal and maximal solutions of the initial value problem for nonlinear integrodifferential equations of mixed type in Banach space. Two main theorems are obtained and two examples are given.

Sign in / Sign up

Export Citation Format

Share Document