Abstract
Existence and uniqueness of mild and classical solutions are discussed for an abstract second-order evolution problem. The nonlinearity contains a local term and a non-local term. The non-local term is an integral in the form of a convolution of a singular kernel and a regular function involving fractional derivatives. This term may be regarded also as a fractional integral of that regular function. In addition the initial conditions are nonlocal and involve fractional derivatives too.
| Original language | English |
|---|---|
| Pages (from-to) | 1-24 |
| Number of pages | 24 |
| Journal | Electronic Journal of Qualitative Theory of Differential Equations |
| DOIs | |
| State | Published - 2012 |
Keywords
- Cauchy problem
- Cosine family
- Fractional derivative
- Fractional non-local conditions
- Mild solutions
- Second-order abstract problem
ASJC Scopus subject areas
- Applied Mathematics
Fingerprint
Dive into the research topics of 'Mild and classical solutions to a fractional singular second order evolution problem'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver