zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the fractional-order logistic equation. (English) Zbl 1140.34302
The authors investigate the fractional-order logistic equation. They study the stability, existence, uniqueness and numerical approximation of a solution.

MSC:
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
26A33Fractional derivatives and integrals (real functions)
34D20Stability of ODE
WorldCat.org
Full Text: DOI
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, No. 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, No. 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. Scientific computing in chemical engineering II--computational fluid dynamics, reaction engineering, and molecular properties, 217-224 (1999)
[5] Diethelm, K.; Freed, A.: The fracpece subroutine for the numerical solution of differential equations of fractional order. Forschung und wissenschaftliches rechnen 1998, 57-71 (1999)
[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. Proceedings of the 5th hellenic--European conference on computer mathematics and its applications, 117-122 (2002) · 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, No. 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, No. 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 1006.34008
[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, No. 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, No. 11, 336-348 (2004) · Zbl 1068.45008
[16] Gorenflo, R.; Mainardi, F.: Fractional calculus: integral and differential equations of fractional order. Fractals and fractional calculus in continuum mechanics, 223-276 (1997)
[17] Matignon, D.: Stability results for fractional differential equations with applications to control processing. Computational engineering in system application 2, 963 (1996)
[18] Podlubny, I.; El-Sayed, A. M. A.: On two definitions of fractional calculus. (1996)
[19] Podlubny, I.: Fractional differential equations. (1999) · Zbl 0924.34008