English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problemD0+αu(t)+(tu(t))=00u003ctu003c1u(0)=0u(1)=∑i=1m−2βiu(ηi)$$begin{aligned} u0026mathbf{D}_{0+}^{alpha}u(t)+fbigl(t,u(t)bigr)=0,quad 0u003c tu003c 1,  u0026u(0)=0, qquad u(1)= {sum_{i=1}^{m-2}} beta_{i} u(eta_{i}), end{aligned}$$where1u003cαu003c2$1u003calphau003c2$,0u003cβiu003c1$0u003cbeta_{i}u003c1$,i=12…m−2$i=1,2,ldots, m-2$,0u003cη1u003cη2u003c⋯u003cηm−2u003c1$0u003ceta_{1}u003ceta _{2}u003ccdotsu003ceta_{m-2}u003c1$,∑i=1m−2βiηiα−1u003c1$sum_{i=1}^{m-2}beta_{i}eta_{i}^{alpha-1}u003c1$,D0+α$mathbf{D}_{0+}^{alpha}$is the standard Riemann–Liouville derivative. Here our nonlinearity f may be singular atu=0$u=0$. As an application of Green’s function, we give some multiple positive solutions for singular positone and semipositone boundary value problems by means of the Leray–Schauder nonlinear alternative and a fixed point theorem on cones.

Multiple positive solutions to singular positone and semipositone m-point boundary value problems of nonlinear fractional differential equations