Multiplicity of positive solutions for coupled system of fractional differential equation with p-Laplacian two-point BVPs

Abstract

In this paper, we investigate the existence of multiple positive solutions for a coupled system of p-Laplacian fractional order two point boundary value problems,

$$\begin{aligned} \left\{ \begin{array}{ccc} D_{a^+}^{\beta _1}\Big (\phi _{p}\Big (D_{a^+}^{\alpha _1}u(t)\Big )\Big )+f_1(t, u(t), v(t))=0,\quad a<t<b,\\ D_{a^+}^{\beta _2}\Big (\phi _{p}\Big (D_{a^+}^{\alpha _2}v(t)\Big )\Big )+f_2(t, u(t), v(t))=0,\quad a<t<b,\\ \xi u(a)-\eta u'(a)=0,\quad \gamma u(b)+\delta u'(b)=0,~D_{a^+}^{\alpha _1}u(a)=0\\ \xi v(a)-\eta v'(a)=0,\quad \gamma v(b)+\delta v'(b)=0,~D_{a^+}^{\alpha _2}v(a)=0 \end{array} \right. \end{aligned}$$

The approach are based on Avery–Henderson fixed point theorem and six functionals fixed point theorem.