scholarly journals Topological structure of solution set for a class of fractional neutral evolution equations on the half-line

2016 ◽  
Vol 48 (1) ◽  
pp. 1
Author(s):  
Le Hoan Hoa ◽  
Nguyen Ngoc Trong ◽  
Le Xuan Truong
Keyword(s):  
Topological Structure ◽  
Evolution Equations ◽  
Solution Set ◽  
Neutral Evolution ◽  
Half Line ◽  
Fractional Neutral Evolution Equations

scholarly journals On the Aronszajn property for fractional neutral evolution equations with infinite delay on half-line

2020 ◽  
Vol 21 (2) ◽  
pp. 767-790
Author(s):  
Nguyen Ngoc Trong ◽  
◽  
Le Xuan Truong ◽  
Nguyen Thanh Tung ◽  
◽  
...  
Keyword(s):  
Evolution Equations ◽  
Infinite Delay ◽  
Neutral Evolution ◽  
Half Line ◽  
Fractional Neutral Evolution Equations

scholarly journals Approximate Controllability of Fractional Neutral Evolution Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
N. I. Mahmudov
Keyword(s):  
Fixed Point ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Neutral Evolution ◽  
Differential Systems ◽  
Neutral Differential Equations ◽  
Approximately Controllable ◽  
Fractional Neutral Evolution Equations

We discuss the approximate controllability of semilinear fractional neutral differential systems with infinite delay under the assumptions that the corresponding linear system is approximately controllable. Using Krasnoselkii's fixed-point theorem, fractional calculus, and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional neutral differential equations with infinite delay are formulated and proved. The results of the paper are generalization and continuation of the recent results on this issue.

scholarly journals Linear evolution equations on the half-line with dynamic boundary conditions

2021 ◽  
pp. 1-33
Author(s):  
D. A. SMITH ◽  
W. Y. TOH
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Evolution Equations ◽  
Half Line ◽  
Robin Problem ◽  
Dynamic Boundary Conditions ◽  
Transform Method ◽  
Linear Evolution ◽  
Robin Condition ◽  
Linear Evolution Equations

The classical half-line Robin problem for the heat equation may be solved via a spatial Fourier transform method. In this work, we study the problem in which the static Robin condition $$bq(0,t) + {q_x}(0,t) = 0$$ is replaced with a dynamic Robin condition; $$b = b(t)$$ is allowed to vary in time. Applications include convective heating by a corrosive liquid. We present a solution representation and justify its validity, via an extension of the Fokas transform method. We show how to reduce the problem to a variable coefficient fractional linear ordinary differential equation for the Dirichlet boundary value. We implement the fractional Frobenius method to solve this equation and justify that the error in the approximate solution of the original problem converges appropriately. We also demonstrate an argument for existence and unicity of solutions to the original dynamic Robin problem for the heat equation. Finally, we extend these results to linear evolution equations of arbitrary spatial order on the half-line, with arbitrary linear dynamic boundary conditions.

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