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Existence results for fractional impulsive integrodifferential equations in Banach spaces. (English) Zbl 1221.34215
Summary: This paper is mainly concerned with the existence of solutions of first order nonlinear impulsive fractional integrodifferential equations in Banach spaces. The results are obtained by using fixed-point principles. Further, some interesting examples are presented to illustrate the theory.

34K37Functional-differential equations with fractional derivatives
26A33Fractional derivatives and integrals (real functions)
45J05Integro-ordinary differential equations
Full Text: DOI
[1] Ahmad, B.; Nieto, J. J.: Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions, Boundary value problems, 1-11 (2009) · Zbl 1167.45003
[2] Balachandran, K.; Park, D. G.: Existence of solutions of quasilinear integrodifferential evolution equations in Banach spaces, Bulletin of korean mathematical society 46, 691-700 (2009) · Zbl 1188.34076 · doi:10.4134/BKMS.2009.46.4.691
[3] Balachandran, K.; Park, J. Y.: Nonlocal Cauchy problem for abstract fractional semilinear evolution equations, Nonlinear analysis: theory methods and applications 71, 4471-4475 (2009) · Zbl 1213.34008 · doi:10.1016/j.na.2009.03.005
[4] Balachandran, K.; Samuel, F. Paul: Existence of solutions for quasilinear delay integrodifferential equations with nonlocal conditions, Electronic journal of differential equations 2009, No. 6, 1-7 (2009) · Zbl 1173.34353 · emis:journals/EJDE/Volumes/2009/06/abstr.html
[5] Balachandran, K.; Kiruthika, S.: Existence of solutions of abstract fractional impulsive semilinear evolution equations, Electronic journal of qualitative theory of differential equations 4, 1-12 (2010) · Zbl 1201.34091 · emis:journals/EJQTDE/2010/201004.pdf
[6] Balachandran, K.; Trujillo, J. J.: The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces, Nonlinear analysis: theory methods and applications 72, 4587-4593 (2010) · Zbl 1196.34007 · doi:10.1016/j.na.2010.02.035
[7] Balachandran, K.; Uchiyama, K.: Existence of solutions of quasilinear integrodifferential equations with nonlocal condition, Tokyo journal of mathematics 23, 203-210 (2000) · Zbl 0976.45011 · doi:10.3836/tjm/1255958815
[8] Belmekki, M.; Nieto, J. J.; Rodríguez-López, R.: Existence of periodic solutions for a nonlinear fractional differential equation, Boundary value problems, 1-18 (2009) · Zbl 1181.34006 · doi:10.1155/2009/324561
[9] Benchohra, M.; Slimani, B. A.: Existence and uniqueness of solutions to impulsive fractional differential equations, Electronic journal of differential equations 2009, No. 10, 1-11 (2009) · Zbl 1178.34004 · emis:journals/EJDE/Volumes/2009/10/abstr.html
[10] Benchohra, M.; Seba, D.: Impulsive fractional differential equations in Banach spaces, Electronic journal of qualitative theory of differential equations special edition I 8, 1-14 (2009) · Zbl 1189.26005 · emis:journals/EJQTDE/sped1/108.pdf
[11] Bonilla, B.; Rivero, M.; Rodríguez-Germá, L.; Trujillo, J. J.: Fractional differential equations as alternative models to nonlinear differential equations, Applied mathematics and computation 187, 79-88 (2007) · Zbl 1120.34323 · doi:10.1016/j.amc.2006.08.105
[12] Byszewski, L.: Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, Journal of mathematical analysis and applications 162, 494-505 (1991) · Zbl 0748.34040 · doi:10.1016/0022-247X(91)90164-U
[13] Byszewski, L.; Akca, H.: Existence of solutions of a semilinear functional -- differential evolution nonlocal problem, Nonlinear analysis: theory methods and applications 34, 65-72 (1998) · Zbl 0934.34068 · doi:10.1016/S0362-546X(97)00693-7
[14] Caputo, M.: Linear model of dissipation whose Q is almost frequency independent, part II, Geophysical journal of royal astronomical society 13, 529-539 (1967)
[15] Chang, Y. K.; Nieto, J. J.: Existence of solutions for impulsive neutral integro -- differential inclusions with nonlocal initial conditions via fractional operators, Numerical functional analysis and optimization 30, 227-244 (2009) · Zbl 1176.34096 · doi:10.1080/01630560902841146 · http://www.informaworld.com/smpp/./content~db=all~content=a910367252
[16] Delbosco, D.; Rodino, L.: Existence and uniqueness for a nonlinear fractional differential equation, Journal of mathematical analysis and applications 204, 609-625 (1996) · Zbl 0881.34005 · doi:10.1006/jmaa.1996.0456
[17] El-Borai, M. M.: Semigroups and some nonlinear fractional differential equations, Applied mathematics and computation 149, 823-831 (2004) · Zbl 1046.34079 · doi:10.1016/S0096-3003(03)00188-7
[18] El-Sayed, A. M. A.: Fractional order diffusion wave equation, International journal of theoretical physics 35, 311-322 (1996) · Zbl 0846.35001 · doi:10.1007/BF02083817
[19] Gafiychuk, V.; Datsun, B.; Meleshko, V.: Mathematical modeling of time fractional reaction -- diffusion systems, Journal of computational and applied mathematics 220, 215-225 (2008) · Zbl 1152.45008 · doi:10.1016/j.cam.2007.08.011
[20] He, J. H.: Some applications of nonlinear fractional differential equations and their approximations, Bulletin of science and technology 15, 86-90 (1999)
[21] He, J. H.: Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer methods in applied mechanics and engineering 167, 57-68 (1998) · Zbl 0942.76077 · doi:10.1016/S0045-7825(98)00108-X
[22] Hernández, E.; O’regan, D.; Balachandran, K.: On recent developments in the theory of abstract differential equations with fractional derivatives, Nonlinear analysis (2010) · Zbl 1229.34004
[23] Hilfer, R.: Applications of fractional calculus in physics, (2000) · Zbl 0998.26002
[24] Jumarie, G.: An approach via fractional analysis to non-linearity induced by coarse-graining in space, Nonlinear analysis: real world applications 11, 535-546 (2010) · Zbl 1195.37054 · doi:10.1016/j.nonrwa.2009.01.003
[25] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, (2006) · Zbl 1092.45003
[26] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations, (1989) · Zbl 0718.34011
[27] Lakshmikantham, V.; Leela, S.; Vasundhara, J.: Theory of fractional dynamic systems, (2009) · Zbl 1188.37002
[28] Liang, J.; Liu, J.; Xiao, T. J.: Nonlocal Cauchy problems governed by compact operator families, Nonlinear analysis: theory methods and applications 57, 183-189 (2004) · Zbl 1083.34045 · doi:10.1016/j.na.2004.02.007
[29] Luchko, Y. F.; Rivero, M.; Trujillo, J. J.; Velasco, M. P.: Fractional models, non-locality, and complex systems, Computers and mathematics with applications 59, 1048-1056 (2010) · Zbl 1189.37095 · doi:10.1016/j.camwa.2009.05.018
[30] Metzler, R.; Klafter, J.: The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics, Journal of physics A: mathematical and general 37, R161-R208 (2004) · Zbl 1075.82018 · doi:10.1088/0305-4470/37/31/R01
[31] Metzler, R.; Schick, W.; Kilian, H-G.; Nonnenmacher, T. F.: Relaxation in filled polymers: a fractional calculus approach, Journal of chemical physics 103, 7180-7186 (1995)
[32] Miller, K. S.; Ross, B.: An introduction to the fractional calculus and fractional differential equations, (1993) · Zbl 0789.26002
[33] N’guérékata, G. M.: A Cauchy problem for some fractional abstract differential equation with non local conditions, Nonlinear analysis: theory methods and applications 70, 1873-1876 (2009) · Zbl 1166.34320 · doi:10.1016/j.na.2008.02.087
[34] Podlubny, I.: Fractional differential equations, (1999) · Zbl 0924.34008
[35] Renardy, M.; Hrusa, W. J.; Nohel, J. A.: Mathematical problems in viscoelasticity, (1987) · Zbl 0719.73013
[36] Ryabov, Ya.E.; Puzenko, A.: Damped oscillations in view of the fractional oscillator equation, Physics review B 66, 184201 (2002)
[37] Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integrals and derivatives; theory and applications, (1993) · Zbl 0818.26003