scholarly journals Differential equation approximations of stochastic network processes: An operator semigroup approach

2012 ◽  
Vol 7 (1) ◽  
pp. 43-58 ◽  
Author(s):  
András Bátkai ◽  
◽  
Istvan Z. Kiss ◽  
Eszter Sikolya ◽  
Péter L. Simon ◽  
...  
Keyword(s):  
Differential Equation ◽  
Operator Semigroup ◽  
Stochastic Network ◽  
Semigroup Approach

scholarly journals Trajectory Controllability of the Systems Governed by Hilfer Fractional Systems

YMER Digital ◽  
2021 ◽  
Vol 20 (11) ◽  
pp. 37-46
Author(s):  
Vishant Shah ◽  
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Nonlinear System ◽  
Differential Equations ◽  
Operator Semigroup ◽  
Local Conditions ◽  
Fractional Systems ◽  
Integro Differential Equation ◽  
Gronwall’S Inequality ◽  
Non Local

In this manuscript, we consider a nonlinear system governed by Hilfer fractional integro-differential equations in a Banach space. Using the concept of operator semigroup and Gronwall’s inequality, we have established the trajectory controllability of the integro-differential equation with local and non-local conditions. Finally, we have given an example to illustrate the application of the derived results

SOLVING A NONLINEAR PSEUDO-DIFFERENTIAL EQUATION OF BURGERS TYPE

2008 ◽  
Vol 08 (04) ◽  
pp. 613-624 ◽  
Author(s):  
NIELS JACOB ◽  
ALEXANDER POTRYKUS ◽  
JIANG-LUN WU
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Nonlinear Equations ◽  
Initial Value Problem ◽  
Symbolic Calculus ◽  
Pseudo Differential Operator ◽  
Initial Value ◽  
Semigroup Approach ◽  
Pseudo Differential Equation ◽  
Point Argument

In this paper, we study the initial value problem for a class of nonlinear equations of Burgers type in the following form: [Formula: see text] for u:(t,x) ∈ (0,∞) × ℝn ↦ ℝ, where q(x,D) is a pseudo-differential operator with negative definite symbol. We solve the initial value problem for the equation on ℝn by utilising a fix point argument based upon a combination of semigroup approach and Hoh's symbolic calculus.

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