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On approximate solutions for a class of semilinear fractional-order differential equations in Banach spaces.
- Source :
-
Fixed Point Theory & Applications . 12/20/2017, Vol. 2017 Issue 1, p1-20. 20p. - Publication Year :
- 2017
-
Abstract
- We apply the topological degree theory for condensing maps to study approximation of solutions to a fractional-order semilinear differential equation in a Banach space. We assume that the linear part of the equation is a closed unbounded generator of a $C_{0}$ -semigroup. We also suppose that the nonlinearity satisfies a regularity condition expressed in terms of the Hausdorff measure of noncompactness. We justify the scheme of semidiscretization of the Cauchy problem for a differential equation of a given type and evaluate the topological index of the solution set. This makes it possible to obtain a result on the approximation of solutions to the problem. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16871820
- Volume :
- 2017
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Fixed Point Theory & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 126887417
- Full Text :
- https://doi.org/10.1186/s13663-017-0621-0