Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations
By Ravi P. Agarwal, Donal O'Regan, Svatoslav Stanek. 2010
290 citations recorded by the source corpus.
Abstract In this paper, we investigate the existence of positive solutions for the singular fractional boundary value problem: D α u ( t ) + f ( t , u ( t ) , D μ u ( t ) ) = 0 , u ( 0 ) = u ( 1 ) = 0 , where 1 α 2 , 0 μ ⩽ α − 1 , D α is the standard Riemann–Liouville fractional derivative, f is a positive Caratheodory function and f ( t , x , y ) is singular at x = 0 . By means of a fixed point theorem on a cone, the existence of positive solutions is obtained. The proofs are based on regularization and sequential techniques.
Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/4906ca46d504767f6a1fd781b49e70eb9f2b4c3e
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In Applied Mathematics
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Citations in the corpus
- Existence of Solutions for a Class of Coupled Fractional Differential Systems with Nonlocal Boundary Conditions (2017, background): “x (t) = (1 + τ1t) h (x) + at 1 − a1 I α+θ1 0 ω (η) − t 1 − a1 I α 0+ω (1) + Iα 0+ω (t) , (11)”
- Fractional boundary value problems with singularities in space variables (2012, unknown): “Paper [26] investigates the Dirichlet problem Du + f t, u,Dμu = 0, u(0) = u(1) = 0, where 1 < α < 2, 0 < μ ≤ 1 and f is a Carathéodory function on [0,1]× (0,∞)×R.”
- Existence of Solutions for Fractional Differential Equations with Multi-point Boundary Conditions at Resonance on a Half-line (2011, background): “The research of fractional differential equations on boundary value problems, as one of the focal topics, has attained a great deal of attention from many researchers (see [18] [19] [20] [21] [29] [34]).”
- Positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator (2012, background): “For some recent contributions on fractional differential equations, see for example, [10-28] and the references therein.”