## Existence of fractional neutral functional differential equations.(English)Zbl 1189.34152

Summary: The initial value problem is discussed for a class of fractional neutral functional differential equations and the criteria on existence are obtained.

### MSC:

 34K37 Functional-differential equations with fractional derivatives 26A33 Fractional derivatives and integrals 34K40 Neutral functional-differential equations 45J05 Integro-ordinary differential equations
Full Text:

### References:

 [1] Kilbas, A.A.; Srivastava, H.M.; Trujillo, J.J., () [2] Lakshmikantham, V.; Leela, S.; Vasundhara Devi, J., Theory of fractional dynamic systems, (2009), Cambridge Scientific Publishers · Zbl 1188.37002 [3] Miller, K.S.; Ross, B., An introduction to the fractional calculus and fractional differential equations, (1993), Wiley New York · Zbl 0789.26002 [4] Podlubny, I., Fractional differential equations, (1993), Academic Press New York · Zbl 0918.34010 [5] R.P. Agarwal, M. Belmekki, M. Benchohra, Existence results for semilinear functional diferential inclusions involving Riemann-Liuville fractional derivative, Dyn. Contin. Discrete Impuls. Syst. Ser.A Math. Anal. (in press) · Zbl 1198.34178 [6] Agarwal, R.P.; Benchohra, M.; Hamani, S., A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta appl. math., (2008) [7] Benchohra, M.; Henderson, J.; Ntouyas, S.K.; Ouahab, A., Existence results for fractional order functional differential equations with infinite delay, J. math. anal. appl., 338, 1340-1350, (2008) · Zbl 1209.34096 [8] Daftardar-Gejji, V.; Bhalekar, S., Boundary value problems for multi-term fractional differential equations, J. math. anal. appl., 345, 754-765, (2008) · Zbl 1151.26004 [9] Diethelm, K., Analysis of fractional differential equations, J. math. anal. appl., 265, 229-248, (2002) · Zbl 1014.34003 [10] El-Borai, M.M., Semigroups and some nonlinear fractional differential equations, Appl. math. comput., 149, 823-831, (2004) · Zbl 1046.34079 [11] El-Sayed, A.M.A., Nonlinear functional differential equations of arbitrary orders, Nonlinear anal., 33, 181-186, (1998) · Zbl 0934.34055 [12] Kosmatov, N., Integral equations and initial value problems for nonlinear differential equations of fractional order, Nonlinear anal., 70, 2521-2529, (2009) · Zbl 1169.34302 [13] Lakshmikantham, V.; Vatsala, A.S., Basic theory of fractional differential equations, Nonlinear anal., 69, 2677-2682, (2008) · Zbl 1161.34001 [14] Muslim, M., Existence and approximation of solutions to fractional differential equations, Math. comput. modelling, 49, 1164-1172, (2009) · Zbl 1165.34304 [15] Salem, H.A.H., On the existence of continuous solutions for a singular system of non-linear fractional differential equations, Appl. math. comput., 198, 445-452, (2008) · Zbl 1153.26004 [16] J. Vasundhara Devi, V. Lakshmikantham, Nonsmooth analysis and fractional differential equations, Nonlinear Anal. (in press) · Zbl 1237.49022 [17] Zhou, Yong, Existence and uniqueness of fractional functional differential equations with unbounded delay, Int. J. dyn. syst. differ. equs., 1, 4, 239-244, (2008) · Zbl 1175.34081 [18] Zhou, Yong; Jiao, Feng; Li, Jing, Existence and uniqueness for $$p$$-type fractional neutral differential equations, Nonlinear anal., 71, 2724-2733, (2009) · Zbl 1175.34082 [19] Zhou, Yong; Jiao, Feng; Li, Jing, Existence and uniqueness for fractional neutral differential equations with infinite delay, Nonlinear anal., 71, 3249-3256, (2009) · Zbl 1177.34084 [20] Lakshmikantham, V., Theory of fractional functional differential equations, Nonlinear anal., 69, 3337-3343, (2008) · Zbl 1162.34344
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.