Gunerhan, HatiraYigider, MuhammedManafian, JalilIlhan, Onur Alp2026-03-262026-03-2620210972-05022169-012X10.1080/09720502.2021.19183192-s2.0-85109682141https://doi.org/10.1080/09720502.2021.1918319https://hdl.handle.net/20.500.14901/1658Günerhan, Hatira/0000-0002-7802-477X; Ilhan, Onur Alp/0000-0003-1618-6439In this study, a nonlinear fractional logistic equations is proposed in the context of a modified form of the conformable fractional-order derivative. The analytical and approximate-analytical solutions are obtained for the proposed mathematical model via the method of conformable fractional differential transform method (CFDTM) and all obtained results have been analyzed and compared with homotopy perturbation method (HPM). With plotting the figures, we compared the CFDTM, HPM, and exact solution together and conclude that the CFDTM solution is closer than the exact solution in comparison with the HPM. The methods are illustrated by two examples of FOLE and solution is obtained. All obtained solutions have been analyzed and compared graphically to validate the effiency and applicability of all results.eninfo:eu-repo/semantics/closedAccessConformable Fractional Differential Transform MethodFractional Order Logistic EquationsCaputo Fractional DerivativeFast Convergent SeriesApproximate SolutionArticle