El-Sayed, A. M. A.; El-Mesiry, A. E. M.; El-Saka, H. A. A. On the fractional-order logistic equation. (English) Zbl 1140.34302 Appl. Math. Lett. 20, No. 7, 817-823 (2007). The authors investigate the fractional-order logistic equation. They study the stability, existence, uniqueness and numerical approximation of a solution. Reviewer: Samir B. Hadid (Ajman) Cited in 2 ReviewsCited in 112 Documents MSC: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 26A33 Fractional derivatives and integrals 34D20 Stability of solutions to ordinary differential equations Keywords:Fractional derivatives and integrals; Integral equations Software:FracPECE PDF BibTeX XML Cite \textit{A. M. A. El-Sayed} et al., Appl. Math. Lett. 20, No. 7, 817--823 (2007; Zbl 1140.34302) Full Text: DOI OpenURL References: [1] Ahmed, E.; El-Sayed, A.M.A.; El-Mesiry, E.M.; El-Saka, H.A.A., Numerical solution for the fractional replicator equation, Internat. J. modern phys. C., 16, 7, 1-9, (2005) · Zbl 1080.65536 [2] Ahmed, E.; El-Sayed, A.M.A.; El-Saka, H.A.A., On some routh – hurwitz conditions for fractional order differential equations and their applications in Lorenz, Rössler, Chua and Chen systems, Phys. lett. A, 358, 1, (2006) · Zbl 1142.30303 [3] Ahmed, E.; El-Sayed, A.M.A.; El-Saka, H.A.A., Equilibrium points, stability and numerical solutions of fractional-order predator – prey and rabies models, J. math. anal. appl., 325, 542-553, (2007) · Zbl 1105.65122 [4] Diethelm, K.; Freed, A., On the solution of nonlinear fractional order differential equations used in the modelling of viscoplasticity, (), 217-224 [5] Diethelm, K.; Freed, A., The fracpece subroutine for the numerical solution of differential equations of fractional order, (), 57-71 [6] K. Diethelm, N.J. Ford, The numerical solution of linear and non-linear fractional differential equations involving fractional derivatives several of several orders, Numerical Analysis Report 379, Manchester Center for Numerical Computational Mathematics [7] Diethelm, K., Predictor – corrector strategies for single- and multi-term fractional differential equations, (), 117-122, [Zbl. Math. 1028.65081] · Zbl 1028.65081 [8] Diethelm, K.; Ford, N.J.; Freed, A.D., A predictor – corrector approach for the numerical solution of fractional differential equations, Nonlinear dyn., 29, 3-22, (2002) · Zbl 1009.65049 [9] Diethelm, K.; Ford, N.J.; Freed, A.D., Detailed error analysis for a fractional Adams method, Numer. algorithms, 36, 31-52, (2004) · Zbl 1055.65098 [10] El-Mesiry, E.M.; El-Sayed, A.M.A.; El-Saka, H.A.A., Numerical methods for multi-term fractional (arbitrary) orders differential equations, Appl. math. comput., 160, 3, 683-699, (2005) · Zbl 1062.65073 [11] El-Sayed, A.M.A., Fractional differential – difference equations, J. fract. calc., 10, 101-106, (1996) · Zbl 0888.34060 [12] El-Sayed, A.M.A., Nonlinear functional differential equations of arbitrary orders, Nonlinear anal., 33, 2, 181-186, (1998) · Zbl 0934.34055 [13] El-Sayed, A.M.A.; Gaafar, F.M., Fractional order differential equations with memory and fractional-order relaxation – oscillation model, Pure math. appl., 12, (2001) · Zbl 0895.34003 [14] El-Sayed, A.M.A.; El-Mesiry, E.M.; El-Saka, H.A.A., Numerical solution for multi-term fractional (arbitrary) orders differential equations, Comput. appl. math., 23, 1, 33-54, (2004) · Zbl 1213.34025 [15] El-Sayed, A.M.A.; Gaafar, F.M.; Hashem, H.H., On the maximal and minimal solutions of arbitrary orders nonlinear functional integral and differential equations, Math. sci. res. J., 8, 11, 336-348, (2004) · Zbl 1068.45008 [16] Gorenflo, R.; Mainardi, F., Fractional calculus: integral and differential equations of fractional order, (), 223-276 [17] Matignon, D., Stability results for fractional differential equations with applications to control processing, (), 963 [18] Podlubny, I.; El-Sayed, A.M.A., On two definitions of fractional calculus, ISBN: 80-7099-252-2, (1996), Solvak Academy of science-institute of experimental phys, UEF-03-96 [19] Podlubny, I., Fractional differential equations, (1999), Academic Press · Zbl 0918.34010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.