scholarly journals Systems of abstract time-fractional equations

2014 ◽  
Vol 95 (109) ◽  
pp. 119-132 ◽  
Author(s):  
Marko Kostic
Keyword(s):  
Semigroups Of Operators ◽  
Locally Convex Spaces ◽  
Fractional Equations ◽  
Locally Convex ◽  
Resolvent Families ◽  
Convex Spaces

We analyze systems of abstract time-fractional equations in certain classes of sequentially complete locally convex spaces. We also consider arbitrary matrices of operators as generators of fractional regularized resolvent families, improving in such a way the results known for semigroups of operators.

Abstract time-fractional equations: Existence and growth of solutions

2011 ◽  
Vol 14 (2) ◽  
Author(s):  
Marko Kostić
Keyword(s):  
Sufficient Conditions ◽  
Existence Theory ◽  
Locally Convex Spaces ◽  
Growth Order ◽  
Fractional Equations ◽  
Locally Convex ◽  
Resolvent Families ◽  
Growth Of Solutions ◽  
Convex Spaces

AbstractWe contribute to the existence theory of abstract time-fractional equations by stating the sufficient conditions for generation of not exponentially bounded α-times C-regularized resolvent families (α > 1) in sequentially complete locally convex spaces. We also consider the growth order of constructed solutions.

scholarly journals Degenerate abstract Volterra equations in locally convex spaces

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 597-619
Author(s):  
Marko Kostic
Keyword(s):  
Resolvent Operator ◽  
Final Section ◽  
Differential Operators ◽  
Volterra Equations ◽  
Locally Convex Spaces ◽  
Efficient Tool ◽  
Scalar Type ◽  
Locally Convex ◽  
Resolvent Families ◽  
Convex Spaces

In the paper under review, we analyze various types of degenerate abstract Volterra integrodifferential equations in sequentially complete locally convex spaces. From the theory of non-degenerate equations, it is well known that the class of (a,k)-regularized C-resolvent families provides an efficient tool for dealing with abstract Volterra integro-differential equations of scalar type. Following the approach of T.-J. Xiao and J. Liang [41]-[43], we introduce the class of degenerate exponentially equicontinuous (a,k)- regularized C-resolvent families and discuss its basic structural properties. In the final section of paper, we will look at generation of degenerate fractional resolvent operator families associated with abstract differential operators.

Representation of complex powers of C-sectorial operators

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Chuang Chen ◽  
Marko Kostić ◽  
Miao Li
Keyword(s):  
Linear Operators ◽  
Locally Convex Spaces ◽  
Sectorial Operators ◽  
Complex Powers ◽  
Locally Convex ◽  
Resolvent Families ◽  
Closed Linear Operators ◽  
Convex Spaces

AbstractThe paper is devoted to the study of representation of complex powers of closed linear operators whose negatives generate equicontinuous (g α, C)-regularized resolvent families (0 < α ≤ 2) on sequentially complete locally convex spaces. Several interesting formulas regarding powers and their domains are proved.

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