Geodesic
Solvability of singular fractional order elastic beam systems with nonlinearities depending on lower derivatives
Yuji Liu 1   ; Shengping Chen 2
1 Department of Mathematics Guangdong University of Finance and Economics Guangzhou 510320, P.R. China
2 Department of Mathematics Guangdong University of Finance and Economics Guangzhou 510320, P.R.China
Applicationes Mathematicae, Tome 43 (2016) no. 2, pp. 235-275 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am2248-4-2016
Keywords: article existence results positive solutions class boundary value problems singular fractional order elastic beam systems nonlinearities depending lower derivatives established nonlinearities fractional differential equations may singular weighted function space constructed complete continuity nonlinear operator proved analysis relies known fixed point theorem

Yuji Liu  1   ; Shengping Chen  2

1 Department of Mathematics Guangdong University of Finance and Economics Guangzhou 510320, P.R. China
2 Department of Mathematics Guangdong University of Finance and Economics Guangzhou 510320, P.R.China 
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     title = {Solvability of singular fractional order elastic beam systems with nonlinearities depending on lower derivatives},
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Yuji Liu; Shengping Chen. Solvability of singular fractional order elastic beam systems with nonlinearities depending on lower derivatives. Applicationes Mathematicae, Tome 43 (2016) no. 2, pp. 235-275. doi: 10.4064/am2248-4-2016

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