Existence and uniqueness of monotone positive solutions for fractional higher-order BVPs. (English) Zbl 1445.34035

Summary: We discuss the existence and uniqueness of monotone positive solutions for a class of higher-order nonlinear fractional differential equations with infinite-point boundary value problems on cones. The existence and uniqueness of solutions are obtained via applying the properties of the Green function and a fixed point theorem. Our analysis is based on the operator equation \(T \omega + S \omega = \omega\) on an ordered Banach space. Finally, a example is given to illustrate our results.


34A08 Fractional ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B27 Green’s functions for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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