Lakshmikantham, V. Theory of fractional functional differential equations. (English) Zbl 1162.34344 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 10, 3337-3343 (2008). Summary: The basic theory for the initial value problems for fractional functional differential equations is considered, extending the corresponding theory of ordinary functional differential equations. Cited in 315 Documents MSC: 34K05 General theory of functional-differential equations Keywords:fractional functional differential equations; local and global existence; theory of inequalities and extremal solutions × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Caputo, M., Linear models of dissipation whose Q is almost independent, II, Geophys. J. R. 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. Comp., 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, (Keil, F.; Mackens, W.; Vob, H.; Werther, J., Scientific Computing in Chemical Engineering II: Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties (1999), Heidelberg: Heidelberg Springer), 217-224 [6] Kiryakova, V., Generalized fractional calculus and applications, (Pitman Res. Notes Math. Ser., vol. 301 (1994), Longman-Wiley: Longman-Wiley New York) · Zbl 1189.33034 [7] Lakshmikantham, V.; Leela, S., (Differential and Integral Inequalities, vol. I and II (1969), Academic Press: Academic Press New York) · Zbl 0177.12403 [8] V. Lakshmikantham, A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal.: TMA (in press); V. Lakshmikantham, A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal.: TMA (in press) · Zbl 1161.34001 [9] V. Lakshmikantham, A.S. Vatsala, Theory of fractional differential inequalities and applications, Commun. Appl. Anal. (in press); V. Lakshmikantham, A.S. Vatsala, Theory of fractional differential inequalities and applications, Commun. Appl. Anal. (in press) · Zbl 1159.34006 [10] V. Lakshmikantham, A.S. Vatsala, General uniqueness and monotone iterative technique for fractional differential equations, Math. Lett. (in press); V. Lakshmikantham, A.S. Vatsala, General uniqueness and monotone iterative technique for fractional differential equations, Math. Lett. (in press) · Zbl 1161.34031 [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: 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: Gordon and Breach Yverdon · Zbl 0818.26003 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.