On the fractional-order logistic equation

By A. El-Sayed, A. El-Mesiry, H. El-Saka. Applied Mathematics Letters, 2007

348 citations recorded by the source corpus.

Abstract The topic of fractional calculus (derivatives and integrals of arbitrary orders) is enjoying growing interest not only among mathematicians, but also among physicists and engineers (see [E.M. El-Mesiry, A.M.A. El-Sayed, H.A.A. El-Saka, Numerical methods for multi-term fractional (arbitrary) orders differential equations, Appl. Math. Comput. 160 (3) (2005) 683–699; A.M.A. El-Sayed, Fractional differential–difference equations, J. Fract. Calc. 10 (1996) 101–106; A.M.A. El-Sayed, Nonlinear functional differential equations of arbitrary orders, Nonlinear Anal. 33 (2) (1998) 181–186; A.M.A. El-Sayed, F.M. Gaafar, Fractional order differential equations with memory and fractional-order relaxation–oscillation model, (PU.M.A) Pure Math. Appl. 12 (2001); A.M.A. El-Sayed, E.M. El-Mesiry, H.A.A. El-Saka, Numerical solution for multi-term fractional (arbitrary) orders differential equations, Comput. Appl. Math. 23 (1) (2004) 33–54; A.M.A. El-Sayed, F.M. Gaafar, H.H. Hashem, On the maximal and minimal solutions of arbitrary orders nonlinear functional integral and differential equations, Math. Sci. Res. J. 8 (11) (2004) 336–348; R. Gorenflo, F. Mainardi, Fractional calculus: Integral and differential equations of fractional order, in: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer, Wien, 1997, pp. 223–276; D. Matignon, Stability results for fractional differential equations with applications to control processing, in: Computational Engineering in System Application, vol. 2, Lille, France, 1996, p. 963; I. Podlubny, A.M.A. El-Sayed, On Two Definitions of Fractional Calculus, Solvak Academy of science-institute of experimental phys, ISBN: 80-7099-252-2, 1996. UEF-03-96; I. Podlubny, Fractional Differential Equations, Academic Press, 1999] for example). In this work we are concerned with the fractional-order logistic equation. We study here the stability, existence, uniqueness and numerical solution of the fractional-order logistic equation.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/798420a2ec2fe3942e485c1f604dba588585313b

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Citations in the corpus

Dynamical behaviors of fractional-order Lotka–Volterra predator–prey model and its discretization (2014, methodology): “For these reasons, FOD have been successfully applied in mathematical biology [5–7] and some other interdisciplinary fields [8–11].”
The Fractional-order SIR and SIRS Epidemic Models with Variable Population Size (2013, positive): “Let α ∈ (0,1] and consider the system ([1,2,3,11,12,13]) D∗ y1(t) = f1(y1,y2,y3), D∗ y2(t) = f2(y1,y2,y3), D∗ y3(t) = f3(y1,y2,y3), (3)”
Numerical treatment for solving fractional Riccati differential equation (2013, neutral): “Also we can deduce that [26] Ið1 u2ðtÞÞjt1⁄40 1⁄4 0: Now from Eq.”
On a discretization process of fractional-order Logistic differential equation (2014, background): “For the existence of solutions for fractional differential equations, one can see [1,2].”
Logistic map with memory from economic model (2017, neutral): “Solution of equation is discussed in [20, 21, 22].”
Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q-differences (2012, background): “Recently, an increasing interest in studying the existence of solutions for boundary value problems of fractional order functional differential equations has been observed [1–10].”
Positive solutions for boundary value problems of nonlinear fractional differential equation (2009, neutral): “[6,7] and C.”
Existence of solutions to fractional order ordinary and delay differential equations and applications. (2011, background): “For the existence of solutions for fractional differential equations, one can see [13, 12, 14, 3, 6, 8, 9, 10, 15, 16, 20, 21, 22, 25, 26, 40] and references therein.”
Analysis of some generalized ABC – Fractional logistic models (2019, background): “Many researchers have discussed the logistic equation in the framework of differenet fractional derivatives (see [24, 25, 26, 27].”