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Weighted Stepanov-like pseudo-almost automorphic mild solutions for semilinear fractional differential equations.
- Source :
-
Advances in Difference Equations . 9/16/2015, Vol. 2015 Issue 1, p1-36. 36p. - Publication Year :
- 2015
-
Abstract
- This work is concerned with the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a class of semilinear fractional differential equations, $D_{t}^{\alpha}x(t)=Ax(t)+D_{t}^{\alpha-1}F(t,x(t))$, $t\in \mathbb{R}$, where $1<\alpha<2$, A is a linear densely defined operator of sectorial type of $\omega<0$ on a complex Banach space X and F is an appropriate function defined on phase space. The fractional derivative is understood in the Riemann-Liouville sense. The results obtained are utilized to study the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a fractional relaxation-oscillation equation. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16871839
- Volume :
- 2015
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Advances in Difference Equations
- Publication Type :
- Academic Journal
- Accession number :
- 109465081
- Full Text :
- https://doi.org/10.1186/s13662-015-0410-1