scholarly journals Fractional Integro-Dierential Equations of Mixed Type with Solution Operator and Optimal Controls

2011 ◽  
Vol 3 (3) ◽  
Author(s):  
Wichai Wittayakiattilerd ◽  
A. Chonwerayuth
Keyword(s):  
Mixed Type ◽  
Solution Operator ◽  
Optimal Controls ◽  
Equations Of Mixed Type

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 Existence of Solutions of Nonlinear Stochastic Volterra Fredholm Integral Equations of Mixed Type

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
K. Balachandran ◽  
J.-H. Kim
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Mixed Type ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Sufficient Conditions ◽  
Fredholm Integral Equations ◽  
Equations Of Mixed Type ◽  
Stochastic Integral Equations

We establish sufficient conditions for the existence and uniqueness of random solutions of nonlinear Volterra-Fredholm stochastic integral equations of mixed type by using admissibility theory and fixed point theorems. The results obtained in this paper generalize the results of several papers.

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