Cabada Fernández, AlbertoWanassi, Om Kalthoum2020-04-292020-04-292020Cabada, A.; Wanassi, O.K. Existence Results for Nonlinear Fractional Problems with Non-Homogeneous Integral Boundary Conditions. Mathematics 2020, 8, 255.http://hdl.handle.net/10347/21883This paper deals with the study of the existence and non-existence of solutions of a three-parameter family of nonlinear fractional differential equation with mixed-integral boundary value conditions. We consider the α -Riemann-Liouville fractional derivative, with α∈(1,2] . To deduce the existence and non-existence results, we first study the linear equation, by deducing the main properties of the related Green functions. We obtain the optimal set of parameters where the Green function has constant sign. After that, by means of the index theory, the nonlinear boundary value problem is studied. Some examples, at the end of the paper, are showed to illustrate the applicability of the obtained resultseng© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)http://creativecommons.org/licenses/by/4.0/Fractional EquationsGreen FunctionsIntegral Boundary ConditionsFixed-Point IndexExistence And Non-Existencejournal article10.3390/math80202552227-7390open access