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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We study the three-point boundary value problem of higher-order fractional differential equations of the form Dc0+ρut+ft, ut=0, 0<t<1, 2⩽n-1<ρ<n, u′(0)=u′′(0)=⋯=un-1(0)=0, u(1)+pu′(1)=qu′(ξ), where cD0+ρ is the Caputo fractional derivative of order ρ, and the function f:[0,1]×[0,∞)↦[0,+∞) is continuously differentiable. Here, 0⩽q⩽p, 0<ξ<1, 2⩽n-1<ρ<n. By virtue of some fixed point theorems, some sufficient criteria for the existence and multiplicity results of positive solutions are established and the obtained results also guarantee that the positive solutions discussed are monotone and concave.

Monotone and Concave Positive Solutions to Three-Point Boundary Value Problems of Higher-Order Fractional Differential Equations