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Existence of positive solutions of nonlinear fractional differential equations. (English) Zbl 1027.34003
The authors consider fractional differential equations based on fractional differential operators of Riemann-Liouville type. The equations considered contain a linear multiterm fractional differential operator. The authors give sufficient conditions for the equation to have positive solutions in four theorems (relating to slightly different conditions in each case). In the last part of the paper, they consider also the question of whether the equations have a unique positive solution.

34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
26A33Fractional derivatives and integrals (real functions)
34K12Growth, boundedness, comparison of solutions of functional-differential equations
Full Text: DOI
[1] Zhang, S.: The existence of a positive solution for a nonlinear fractional differential equation. J. math. Anal. appl. 252, 804-812 (2000) · Zbl 0972.34004
[2] Naito, M.; Yano, K.: Positive solutions of higher order ordinary differential equations with general nonlinearities. J. math. Anal. appl. 250, 27-48 (2000) · Zbl 0967.34004
[3] Wang, J.: On positive solutions of singular nonlinear two-point boundary value problems. J. differential equations 107, 163-174 (1994) · Zbl 0792.34023
[4] Choi, Y. S.; Kim, E. H.: On the existence of positive solutions of quasilinear elliptic boundary value problems. J. differential equations 155, 423-442 (1999) · Zbl 0946.35033
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[6] Samko, S.; Kilbas, A.; Marichev, O.: Fractional integrals and derivatives. (1993) · Zbl 0818.26003
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