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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.

MSC:
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