Cabada Fernández, AlbertoWanassi, Om Kalthoum2024-11-252024-11-252021-02-02Cabada, A., Wanassi, O.K. Extremal solutions of nonlinear functional discontinuous fractional equations. Comp. Appl. Math. 40, 36 (2021). https://doi.org/10.1007/s40314-020-01397-z2238-3603https://hdl.handle.net/10347/37813This version of the article has been accepted for publication, after peer review, and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s40314-020-01397-zThis paper is devoted to prove the existence of extremal solutions of Fractional equation with Riemann-Liouville derivative. The existence follows from the method of lower and upper solutions. Some jumps in the derivative of these functions are allowed. It is important to point out that a discontinuous and functional dependence on the nonlinear part of the equation with respect to the solution is allowed. The construction of the Green’s function related to the linear part of the equation coupled to spectral theory is fundamental to deduce the results.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Lower and Upper SolutionsGreen's FunctionsDiscontinuous EquationsFunctional EquationsComparison Principles1202 Análisis y análisis funcionaljournal article10.1007/s40314-020-01397-z1807-0302open access