Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions. (English) Zbl 1484.34080

Ardjouni, Abdelouaheb

AIMS Math. 4, No. 4, 1101-1113 (2019).

Summary: In this paper, we prove the existence and uniqueness of a positive solution of nonlinear Hadamard fractional differential equations with integral boundary conditions. In the process we employ the Schauder and Banach fixed point theorems and the method of upper and lower solutions to show the existence and uniqueness of a positive solution. Finally, an example is given to illustrate our results.

MSC:

34B18	Positive solutions to nonlinear boundary value problems for ordinary differential equations
34A08	Fractional ordinary differential equations
34B10	Nonlocal and multipoint boundary value problems for ordinary differential equations

Keywords:

fractional differential equations; positive solutions; upper and lower solutions; existence; uniqueness; fixed point theorems

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