Abstract
In this paper, we study the following fractional Navier boundary value problem
where \(\alpha ,\beta \in (0,1]\) such that \(\alpha +\beta >1\), \(D^{\beta }\) and \(D^{\alpha }\) stand for the standard Riemann–Liouville fractional derivatives and a, b are nonnegative constants such that \(a+b>0\). The function g is a nonnegative continuous function in \([0,\infty )\) that is required to satisfy some suitable integrability condition. Using estimates on the Green’s function and a perturbation argument, we prove the existence of a unique positive continuous solution, which behaves like the unique solution of the homogeneous problem.
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Mâagli, H., Dhifli, A. & Alzahrani, A.K. Existence Result for a Superlinear Fractional Navier Boundary Value Problems. Mediterr. J. Math. 15, 68 (2018). https://doi.org/10.1007/s00009-018-1114-z
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DOI: https://doi.org/10.1007/s00009-018-1114-z