### Systems of singularly perturbed fractional integral equations

Angelina M. Bijura
Source: J. Integral Equations Appl. Volume 24, Number 2 (2012), 195-211.
First Page:
Primary Subjects: 45D05, 45F15, 26A33, 34E15, 33E12
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Permanent link to this document: http://projecteuclid.org/euclid.jiea/1340369462
Digital Object Identifier: doi:10.1216/JIE-2012-24-2-195
Zentralblatt MATH identifier: 06085057
Mathematical Reviews number (MathSciNet): MR2945802

### References

E. Ahmed and A.S. Elgazzar, On fractional order differential equations model for nonlocal epidemics, Phys. A 379 (2007), 607-614.
E. Ahmed and H.A. El-Saka, On fractional order models for Hepatitis C, Nonlinear Biomed. Phys. 4 (2010), www.nonlinearbiomedphys.com/content/4/1/1.
–––, On modeling two immune effectors two strain antigen interaction, Nonlinear Biomed. Phys. 4 (2010), www.nonlinearbiomedphys.com/content/4/1/6/.
J.S. Angell and W.E. Olmstead, Singularly perturbed Volterra integral equations, SIAM J. Appl. Math. 47 (1987), 1-14.
Mathematical Reviews (MathSciNet): MR873233
Digital Object Identifier: doi:10.1137/0147001
–––, Singularly perturbed Volterra integral equations II, SIAM J. Appl. Math. 47 (1987), 1150-1162.
Mathematical Reviews (MathSciNet): MR916233
Zentralblatt MATH: 0635.45023
Digital Object Identifier: doi:10.1137/0147077
A.M. Bijura, Singularly perturbed Volterra integral equations with weakly singular kernels, Internat. J. Math. Math. Sci. 30 (2002), 129-143.
Mathematical Reviews (MathSciNet): MR1905416
Zentralblatt MATH: 1001.45001
Digital Object Identifier: doi:10.1155/S016117120201325X
–––, Asymptotics of integro-differential models with integrable kernels, Int. J. Math. Math. Sci. 2003 (2003), 1577-1798.
–––, Asymptotics of integro-differential models with integrable kernels II, Int. J. Math. Math. Sci. 2003 (2003), 3153-3170.
–––, Error bound analysis & singularly perturbed Abel-Volterra equations, J. Appl. Math. 2004 (2004), 479-494.
Mathematical Reviews (MathSciNet): MR2200995
Zentralblatt MATH: 1081.45001
Digital Object Identifier: doi:10.1155/S1110757X04305024
–––, Transcendental smallness in singularly perturbed equations of Volterra type, African Diaspora J. Math. 3 (2005), 1-20.
Mathematical Reviews (MathSciNet): MR2244118
Zentralblatt MATH: 1106.45001
–––, Initial layer theory and model equations of Volterra type, IMA J. Appl. Math. 71 (2006), 315-331.
Mathematical Reviews (MathSciNet): MR2228907
Zentralblatt MATH: 1123.45002
Digital Object Identifier: doi:10.1093/imamat/hxh113
A.M. Bijura, Nonlinear singular perturbation problem of fractional orders, African Diaspora J. Math. 7 (2008), 165-180.
Mathematical Reviews (MathSciNet): MR2530832
Zentralblatt MATH: 1182.26008
W. Chen, Nonlinear dynamics and chaos in a fractional-order financial system, Chaos Solitons Fractals 36 (2008), 1305-1314.
G. Doetsch, Guide to the Applications of the Laplace and $Z$-transforms, Van Nostrand Reinhold Company, London, 1961, 1971.
A. Erdélyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Higher transcendental functions, Vol. 3, McGraw-Hill Book Co., New York, 1955.
Mathematical Reviews (MathSciNet): MR66496
G.I. Eskin, Boundary value problems for elliptic pseudodifferential equations, Transl. Math. Mono. 52 American Mathematical Society, 1981.
Mathematical Reviews (MathSciNet): MR623608
Y. Haiping and D. Yongsheng, Nonlinear dynamics and chaos in a fractional-order HIV model, Math. Probl. Eng. 2009 (2009), doi:10.1155/2009/378614.
Mathematical Reviews (MathSciNet): MR2530065
Zentralblatt MATH: 1181.37124
R. Hilfer, ed., Applications of factional calculus in physics, World Scientific, River Edge, NJ, 2000.
Mathematical Reviews (MathSciNet): MR1890104
J.-P. Kauthen, A survey on singularly perturbed Volterra equations, Appl. Numer. Math. 24 (1997), 95-114.
Mathematical Reviews (MathSciNet): MR1464717
Digital Object Identifier: doi:10.1016/S0168-9274(97)00014-7
A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equations, Vol. 204, North-Holland Mathematics Studies, Elsevier, Amsterdam, 2006.
Mathematical Reviews (MathSciNet): MR2218073
Zentralblatt MATH: 1092.45003
F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, in Fractals and fractional calculus in continuum mechanics, A. Carpinteri and F. Mainardi, eds., Springer-Verlag, Wien, 1997.
Mathematical Reviews (MathSciNet): MR1611587
R.E. O'Malley, Introduction to singular perturbation, Academic Press, New York, 1974.
Mathematical Reviews (MathSciNet): MR402217
–––, Singular perturbation methods for ordinary differential equations, Springer-Verlag, New York, 1991.
Mathematical Reviews (MathSciNet): MR1123483
I. Podlubny, Fractional differential equations, Academic Press, San Diego, CA, 1999.
Mathematical Reviews (MathSciNet): MR1658022
S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional integral and derivatives: Theory and application, Gordon and Breach Science Publishers, Switzerland, 1993.
Mathematical Reviews (MathSciNet): MR1347689
R. Schumer, M.M. Meerschaert and B. Baeumer, Fractional advection-dispersion equations for modeling transport at the Earth surface, J. Geograph. Research 114 (2009), p.F00A07, doi:10.1029/2008JF001246.
L.A. Skinner, Asymptotic solution to a class of singularly perturbed Volterra integral equations, Methods Appl. Anal. 2 (1995), 212-221.
Mathematical Reviews (MathSciNet): MR1350897
Zentralblatt MATH: 0840.45006
D.R. Smith, Singular perturbation theory; An introduction with applications, Cambridge University Press, Cambridge, New York, 1985.
Mathematical Reviews (MathSciNet): MR812466
E.J. Watson, Laplace transforms and applications, Van Nostrand Reinhold Company, Ltd., New York, 1981. \noindentstyle
Mathematical Reviews (MathSciNet): MR622023
Zentralblatt MATH: 0453.44007