ASYMPTOTICALLY ALMOST PERIODIC SOLUTIONS OF SOME LINEAR EVOLUTION EQUATIONS

1988 ◽  
Vol 61 (1) ◽  
pp. 1-8
Author(s):  
B G Ararktsyan
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Linear Evolution ◽  
Linear Evolution Equations ◽  
Asymptotically Almost Periodic

scholarly journals Asymptotically almost periodic solutions of fractional evolution equations

2021 ◽  
Vol 8 (3) ◽  
pp. 475-483
Author(s):  
Duc Huy Nguyen ◽  
◽  
Trong Luong Vu ◽  
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Initial Boundary ◽  
Asymptotic Behavior Of Solutions ◽  
Operator Family ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Fractional Evolution Equations ◽  
Exponentially Stable ◽  
Asymptotically Almost Periodic

We study the asymptotic behavior of solutions of nonlinear fractional evolution equations in Banach spaces. Asymptotically almost periodic solutions on half line are obtained by establishing a sharp estimate on the resolvent operator family of evolution equations. In particular, when the semigroup generated by A is exponentially stable then the conditions of the existence asymptotically almost periodic solutions is satisfied. An application to a fractional partial differential equation with initial boundary condition is also considered.

scholarly journals Asymptotically almost periodic solutions of fractional relaxation inclusions with Caputo derivatives

2018 ◽  
Vol 104 (118) ◽  
pp. 23-41 ◽  
Author(s):  
Marko Kostic
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Fixed Point Theorems ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Coefficients ◽  
Sectorial Operators ◽  
Almost Sectorial Operators ◽  
Fractional Relaxation ◽  
Asymptotically Almost Periodic

We analyze asymptotically almost periodic solutions for a class of (semilinear) fractional relaxation inclusions with Stepanov almost periodic coefficients. As auxiliary tools, we use subordination principles, fixed point theorems and the well known results on the generation of infinitely differentiable degenerate semigroups with removable singularities at zero. Our results are well illustrated and seem to be not considered elsewhere even for fractional relaxation equations with almost sectorial operators.

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