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Existence of solutions of initial value problems for nonlinear fractional differential equations on the half-axis. (English) Zbl 1235.34022
The global existence of solutions on the half-axis for a classical initial value problem of fractional differential equations involving Riemann-Liouville fractional derivative is studied. The authors proof the main results using fixed-point theorems on Banach spaces.
MSC:
34A08Fractional differential equations
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
47N20Applications of operator theory to differential and integral equations
References:
[1]Hilfer, R.: Applications of fractional calculus in physics, (2000)
[2]Gaul, L.; Klein, P.; Kempfle, S.: Damping description involving fractional operators, Mech. syst. Signal process. 5, 81-88 (1991)
[3]Diethelm, K.; Freed, A. D.: On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity, Scientific computing in chemical engineering II-computational fluid dynamics, reaction engineering and molecular properties (1999)
[4]Koeller, R. C.: Application of fractional calculus to the theory of viscoelasticity, J. appl. Mech 51, 299-307 (1984) · Zbl 0544.73052 · doi:10.1115/1.3167616
[5]Kumar, P.; Agrawal, O. P.: An approximate method for numerical solution of fractional differential equations, Signal process. 86, 2602-2610 (2006) · Zbl 1172.94436 · doi:10.1016/j.sigpro.2006.02.007
[6]Podlubny, I.: Geometric and physical interpretation of fractional integration and fractional differentiation, Fract. calc. Appl. anal. 5, 367-386 (2002) · Zbl 1042.26003
[7]Metzler, F.; Schick, W.; Kilian, H. G.; Nonnenmacher, T. F.: Relaxation in filled polymers: a fractional calculus approach, J. chem. Phys. 103, 7180-7186 (1995)
[8]Kilbas, A. A.; Srivastava, Hari M.; Trujillo, Juan J.: Theory and applications of fractional differential equations, North-holland mathematics studies 204 (2006)
[9]Miller, K. S.; Ross, B.: An introduction to the fractional calculus and differential equations, (1993)
[10]Podlubny, I.: Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, (1999)
[11]Lakshmikantham, V.; Leela, S.; Vasundhara, J.: Theory of fractional dynamic systems, (2009)
[12]Lakshmikantham, V.; Vatsala, A. S.: Basic theory of fractional differential equations, Nonlinear anal. 69, 2677-2682 (2008) · Zbl 1161.34001 · doi:10.1016/j.na.2007.08.042
[13]Kilbas, A. A.; Trujillo, J. J.: Differential equations of fractional order: methods, results and problems I, Appl. anal. 78, 153-192 (2001) · Zbl 1031.34002 · doi:10.1080/00036810108840931
[14]Kilbas, A. A.; Trujillo, J. J.: Differential equations of fractional order: methods, results and problems II, Appl. anal. 81, 435-493 (2002) · Zbl 1033.34007 · doi:10.1080/0003681021000022032
[15]Srivastava, H. M.; Saxena, R. K.: Operators of fractional integration and their applications, Appl. math. Comput. 118, 1-52 (2001) · Zbl 1022.26012 · doi:10.1016/S0096-3003(99)00208-8
[16]Agarwal, R. P.; Benchohra, M.; Slimani, B. A.: Existence results for differential equations with fractional order and impulses, mem. Differential equations, Math. phys. 44, 1-21 (2008) · Zbl 1178.26006
[17]Ouahab, A.: Some results for fractional boundary value problem of differential inclusions, Nonlinear anal. 69, 3877-3896 (2008) · Zbl 1169.34006 · doi:10.1016/j.na.2007.10.021
[18]El-Sayed, A. M. A.: On the fractional differential equation, Appl. math. Comput. 49, 205-213 (1992) · Zbl 0757.34005 · doi:10.1016/0096-3003(92)90024-U
[19]El-Sayed, A. M. A.: Fractional order diffusion-wave equations, Internat. J. Theoret. phys. 35, 311-322 (1996) · Zbl 0846.35001 · doi:10.1007/BF02083817
[20]El-Sayed, A. M. A.: Nonlinear functional differential equations of arbitrary orders, Nonlinear anal. 33, 181-186 (1998) · Zbl 0934.34055 · doi:10.1016/S0362-546X(97)00525-7
[21]Nieto, J. J.: Maximum principles for fractional differential equations derived from Mittag-Leffler functions, Appl. math. Lett. 23, 1248-1251 (2010) · Zbl 1202.34019 · doi:10.1016/j.aml.2010.06.007
[22]Li, C.; Deng, W.: Remarks on fractional derivatives, Appl. math. Comput. 187, 777-784 (2007) · Zbl 1125.26009 · doi:10.1016/j.amc.2006.08.163
[23]Kosmatov, N.: Integral equations and initial value problems for nonlinear differential equations of fractional order, Nonlinear anal. 70, 2521-2529 (2009) · Zbl 1169.34302 · doi:10.1016/j.na.2008.03.037
[24]Muslim, M.; Conca, C.; Nandakumaran, A. K.: Approximate of solutions to fractional integral equation, Comput. math. Appl. 59, 1236-1244 (2010) · Zbl 1189.65310 · doi:10.1016/j.camwa.2009.06.028
[25]Stojanović, M.: Existence-uniqueness result for a nonlinear n-term fractional equation, J. math. Anal. appl. 353, 244-245 (2009) · Zbl 1195.34014 · doi:10.1016/j.jmaa.2008.11.056
[26]Delbosco, D.; Rodino, L.: Existence and uniqueness for a nonlinear fractional differential equation, J. math. Anal. appl. 204, 609-625 (1996) · Zbl 0881.34005 · doi:10.1006/jmaa.1996.0456
[27]Babakhani, A.; Gejji, V. D.: Existence of positive solutions of nonlinear fractional differential equations, J. math. Anal. appl. 278, 434-442 (2003) · Zbl 1027.34003 · doi:10.1016/S0022-247X(02)00716-3
[28]Yu, C.; Gao, G.: Existence of fractional differential equations, J. math. Anal. appl. 310, 26-29 (2005) · Zbl 1088.34501 · doi:10.1016/j.jmaa.2004.12.015
[29]Kou, C. H.; Liu, J.; Ye, Y.: Existence and uniqueness of solutions for the Cauchy-type problems of fractional differential equations, Disc. dyn. Nat. soc. (2010) · Zbl 1197.34004 · doi:10.1155/2010/142175
[30]Kilbas, A. A.; Bonilla, B.; Trujillo, J. J.: Existence and uniqueness theorems for nonlinear fractional differential equations, Demonstratio math. 33, No. 3, 538-602 (2000) · Zbl 0964.34004
[31]Eidelman, S. D.; Kochubei, A. N.: Cauchy problem for fractional diffusion equations, J. differential equations, No. 199, 211-255 (2004) · Zbl 1068.35037 · doi:10.1016/j.jde.2003.12.002
[32]Zhang, S. Q.: Monotone iterative method for initial value problem involving Riemann–louville derivatives, Nonlinear anal. 71, 2087-2093 (2009) · Zbl 1172.26307 · doi:10.1016/j.na.2009.01.043
[33]Wei, Z. L.; Li, Q. D.; Che, J. L.: Initial value problems for fractional differential equations involving Riemann–Liouville sequential fractional derivative, J. math. Anal. appl. 367, 260-272 (2010) · Zbl 1191.34008 · doi:10.1016/j.jmaa.2010.01.023
[34]Zhao, X.; Ge, W.: Unbounded solutions for fractional bounded value problems on the infinite interval, Acta appl. Math. 109, 495-505 (2010) · Zbl 1193.34008 · doi:10.1007/s10440-008-9329-9
[35]Arara, A.; Benchohra, M.; Hamidi, N.; Nieto, J. J.: Fractional order differential equations on an unbounded domain, Nonlinear anal. 72, 580-586 (2010) · Zbl 1179.26015 · doi:10.1016/j.na.2009.06.106
[36]Agarwal, R. P.; Regan, D. O.: Infinite interval problems for differential, difference and integral equations, (2001)
[37]Agarwal, R. P.; Regan, D. O.: Boundary value problems of nonsingular type on the semi-infinite interval, Tohoku. math. J. 51, 391C397 (1999) · Zbl 0942.34026 · doi:10.2748/tmj/1178224769
[38]Granas, A.; Dugundji, J.: Fixed point theory, (2003)