## Solvability of singular fractional order elastic beam systems with nonlinearities depending on lower derivatives

### Volume 43 / 2016

Applicationes Mathematicae 43 (2016), 235-275
MSC: 26A08, 34A08, 34A34, 34A12, 45J08, 34A37, 34R15, 34B40.
DOI: 10.4064/am2248-4-2016
Published online: 9 September 2016

#### Abstract

In this article, existence results for positive solutions of a class of boundary-value problems for singular fractional order elastic beam systems with nonlinearities depending on lower derivatives are established. The nonlinearities in fractional differential equations may be singular at $t=0$ and $t=1$. A weighted function space is constructed and complete continuity of a nonlinear operator is proved. Our analysis relies on a well known fixed point theorem.