On a singular Riemann–Liouville fractional boundary value problem with parameters
Articles
Alexandru Tudorache
Gh. Asachi Technical University
https://orcid.org/0000-0003-0151-505X
Rodica Luca
Gh. Asachi Technical University
https://orcid.org/0000-0003-3901-5747
Published 2021-01-01
https://doi.org/10.15388/namc.2021.26.21414
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Keywords

Riemann–Liouville fractional differential equation
nonlocal boundary conditions
positive parameter
singularities
positive solutions
semipositone problem

How to Cite

Tudorache A. and Luca R. (2021) “On a singular Riemann–Liouville fractional boundary value problem with parameters”, Nonlinear Analysis: Modelling and Control, 26(1), pp. 151-168. doi: 10.15388/namc.2021.26.21414.

Abstract

We investigate the existence of positive solutions for a nonlinear Riemann–Liouville fractional differential equation with a positive parameter subject to nonlocal boundary conditions, which contain fractional derivatives and Riemann–Stieltjes integrals. The nonlinearity of the equation is nonnegative, and it may have singularities at its variables. In the proof of the main results, we use the fixed point index theory and the principal characteristic value of an associated linear operator. A related semipositone problem is also studied by using the Guo–Krasnosel’skii fixed point theorem.

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