Haoues MoussaArdjouni Abdelouaheb2024-05-302024-05-302020-02-23https://dspace.univ-eloued.dz/handle/123456789/32800InterventionWe study the existence and uniqueness of positive solutions of the rst-order nonlinear Liouville Caputo fractional differential equation ........................................................ ........................................................ where ....... In the process we convert the given fractional differential equation into an equivalent integral equation. Then we construct appropriate mappings and employ the Krasnoselskii xed point theorem and the method of upper and lower solutions to show the existence of a positive solution of this equation. We also use the Banach xed point theorem to show the existence of a unique positive solution.enFractional di¤erential equationPositive solutionsFixed point theoremExistence and uniquenessIntervention