a r t i c l e i n f o Keywords: Fractional differential equation Singular problem Riemann-Liouville fractional derivative Riemann-Liouville fractional integral Fixed point theorem on cones a b s t r a c t We discuss the existence of positive solutions for the singular fractional boundary valueHere D α is the standard Riemann-Liouville fractional derivative of order α, f is a Carathéodory function and f (t, x, y, z) is singular at the value 0 of its arguments x, y, z.
a b s t r a c tWe investigate the solvability of the Dirichlet boundary value problemwhere λ is a nonnegative parameter. We discuss the existence of multiple positive solutions and show that for certain values of λ, there also exist solutions that vanish on a subinterval [ρ, 1 − ρ] ⊂ (0, 1), the so-called dead-core solutions. In order to illustrate the theoretical findings, we present computational results for g(u) = 1/ √ u, computed using the collocation method implemented in bvpsuite, a new version of the standard MATLAB code sbvp1.0.
Crown
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