Cabada Fernández, AlbertoKisela, Tomas2026-01-272026-01-272017-03-04Alberto Cabada, Tomáš Kisela, Existence of positive periodic solutions of some nonlinear fractional differential equations, Communications in Nonlinear Science and Numerical Simulation, Volume 50, 2017, Pages 51-67, ISSN 1007-5704, https://doi.org/10.1016/j.cnsns.2017.02.010.1007-5704https://hdl.handle.net/10347/45457The paper is devoted to study of existence and uniqueness of periodic solutions for a particular class of nonlinear fractional differential equations admitting its right-hand side with certain singularities. Our approach is based on Krasnosel’skiĭ and Schauder fixed point theorems and monotone iterative technique which enable us to extend some previously known results. The discussed problems are characterized by a Green’s function which has integrable singularities disallowing a direct use of classical techniques known from theory of ordinary differential equations, therefore proper modifications are proposed. Furher, the paper presents simple numerical algorithms directly built on the iterative technique used in theoretical proofs. Illustrative examples conclude the paper.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Periodic Fractional EquationKrasnosel’skii fixed pointGreen’s functionMonotone Iterative Methods1202 Análisis y análisis funcionaljournal article10.1016/j.cnsns.2017.02.0101878-7274open access