Positive solutions of a singular fractional boundary value problem with a fractional boundary condition

Abstract

Abstract. For α ∈ (1, 2], the singular fractional boundary value problemsatisfying the boundary conditionsRiemann-Liouville derivatives of order α, β and µ respectively, is considered. Here f satisfies a local Carathéodory condition, and f (t, x, y) may be singular at the value 0 in its space variable x. Using regularization and sequential techniques and Krasnosel'skii's fixed point theorem, it is shown this boundary value problem has a positive solution. An example is given.

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