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

• Autorzy: Lyons J. W. , Neugebauer J. T.

Identyfikatory

DOI

10.7494/OpMath.2017.37.3.421

• Języki publikacji: EN

Abstrakty

EN

For α ∈ (1,2] the singular fractional boundary value problem [formula] satisfying the boundary conditions [formula] where β ∈ (0,α - 1], μ ∈ (0,α - 1], and [formula] are Riemann-Liouville derivatives of order α, β, and μ respectively, is considered. Here ƒ satisfies a local Carathéodory condition, and ƒ (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.

Słowa kluczowe

EN

fractional differential equation; singular problem; fixed point

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2017
• Tom: Vol. 37, no. 3
• Strony: 421--434
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Lyons J. W.

• Nova Southeastern University Department of Mathematics Fort Lauderdale, FL 33314 USA

autor

Neugebauer J. T.

• Eastern Kentucky University Department of Mathematics and Statistics Richmond, KY 40475 USA

Bibliografia

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Uwagi

EN

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).