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New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions. (English) Zbl 1214.34005
The paper is concerned with presenting some new existence theorems for positive solutions to fractional boundary value problems of fractional order greater than 3. The main tool in the analysis is a fractional Greens function. The paper is structured as follows: the problem is introduced and the Greens function is defined. The properties of the Greens function are explored and this leads to a section on existence theory for positive solutions. The authors go on to consider the existence of multiple positive solutions. In conclusion, they identify some questions that remain open.
MSC:
34A08Fractional differential equations
34B10Nonlocal and multipoint boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
34B27Green functions
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