POSITIVE SOLUTIONS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN

Authors

  • N. Nyamoradi Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran
  • M. Javidi Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran

Abstract

In this paper, we study the existence of positive solution to boundary value problem for fractional differential equation with a one-dimensional $p$-Laplacian operator
\begin{equation*}
begin{cases}
D_{0^+}^\sigma (\phi_p ( u'' (t))) - g (t) f (u (t)) = 0, t \in (0, 1),\\
\phi_p ( u'' (0)) = \phi_p ( u'' (1)) = 0,\\
a u (0) - b u' (0) = \sum_{i = 1}^{m - 2} a_i u (\xi_i),\\
c u (1) + d u' (1) = \sum_{i = 1}^{m - 2} b_i u (\xi_i),
\end{cases}
\end{equation*}
where $D_{0^+}^\alpha$ is the Riemann-Liouville fractional derivative of order $1 < \sigma \leq 2$, $\phi_p (s) = |s|^{p - 2} s$, $p > 1$ and $f$ is a lower semi-continuous function. By using Krasnoselskii's fixed point theorems in a cone, the existence of one positive solution and multiple positive solutions for nonlinear singular boundary value problems is obtained.

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Published

2012-08-29

How to Cite

Nyamoradi, N., & Javidi, M. (2012). POSITIVE SOLUTIONS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 3(2), 239-253. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/171

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Section

Research Article