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General uniqueness and monotone iterative technique for fractional differential equations. (English) Zbl 1161.34031
The authors present a very interesting work on how can be explored the solution of certain class of hyperbolic evolution equation, with limited smoothness, using multi-scale approaching techniques. The construction considered by the authors in this paper implies a full-wave description. The study suggests a novel computational algorithm. Also the authors present some applications of such numerical approach.

MSC:
34G20 Nonlinear differential equations in abstract spaces
26A33 Fractional derivatives and integrals
34A35 Ordinary differential equations of infinite order
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[1] Caputo, M., Linear models of dissipation whose Q is almost independent, II, Geophys. J. roy. astron., 13, 529-539, (1967)
[2] Glöckle, W.G.; Nonnenmacher, T.F., A fractional calculus approach to self similar protein dynamics, Biophys. J., 68, 46-53, (1995)
[3] Diethelm, K.; Ford, N.J., Analysis of fractional differential equations, J. math. anal. appl., 265, 229-248, (2002) · Zbl 1014.34003
[4] Diethelm, K.; Ford, N.J., Multi-order fractional differential equations and their numerical solution, Appl. math. comput., 154, 621-640, (2004) · Zbl 1060.65070
[5] Diethelm, K.; Freed, A.D., On the solution of nonlinear fractional differential equations used in the modeling of viscoplasticity, (), 217-224
[6] Kiryakova, V., Generalized fractional calculus and applications, () · Zbl 1189.33034
[7] Ladde, G.S.; Lakshmiakntham, V.; Vatsala, A.S., Monotone iterative techniques for nonlinear differential equations, (1985), Pitman Advanced Publishing Program Boston · Zbl 0658.35003
[8] Lakshmikantham, V.; Leela, S., Differential and integral inequalities, vol. I, (1969), Academic Press New York · Zbl 0177.12403
[9] V. Lakshmikantham, A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal. TMA (2007) (in press) · Zbl 1159.34006
[10] V. Lakshmikantham, A.S. Vatsala, Theory of fractional differential inequalities and applications, Commun. Appl. Anal. (2007) (in press) · Zbl 1159.34006
[11] Metzler, R.; Schick, W.; Kilian, H.G.; Nonnenmacher, T.F., Relaxation in filled polymers: A fractional calculus approach, J. chem. phys., 103, 7180-7186, (1995)
[12] Podlubny, I., Fractional differential equations, (1999), Academic Press San Diego · Zbl 0918.34010
[13] Samko, S.G.; Kilbas, A.A.; Marichev, O.I., Fractional integrals and derivatives, theory and applications, (1993), Gordon and Breach Yverdon · Zbl 0818.26003
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