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Existence results for fractional integrodifferential equations with nonlocal condition via resolvent operators. (English) Zbl 1228.34013
Summary: We prove the existence of solutions of fractional integrodifferential equations by using the resolvent operators and fixed point theorem. An example is given to illustrate the abstract results.
MSC:
34A08Fractional differential equations
45K05Integro-partial differential equations
34K05General theory of functional-differential equations
References:
[1]Hilfer, R.: Applications of fractional calculus in physics, (2000)
[2]Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, (2006)
[3]Lakshmikantham, V.; Leela, S.; Devi, J. Vasundhara: Theory of fractional dynamic systems, (2009)
[4]Metzler, F.; Schick, W.; Kilian, H. G.; Nonnenmacher, T. F.: Relaxation in filled polymers: a fractional calculus approach, Journal of chemical physics 103, 7180-7186 (1995)
[5]Miller, K. S.; Ross, B.: An introduction to the fractional calculus and fractional differential equations, (1993)
[6]Podlubny, I.: Fractional differential equations, (1999)
[7]Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integrals and derivatives; theory and applications, (1993) · Zbl 0818.26003
[8]Gafiychuk, V.; Datsko, 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
[9]J. Nakagawa, K. Sakamoto, M. Yamamoto, Overview to mathematical analysis for fractional diffusion equations – new mathematical aspects motivated by industrial collaboration, Journal of Math-for-Industry, 2, 2010A-10, 99–108. · Zbl 1206.35247 · doi:http://gcoe-mi.jp/english/./temp/publish/a3e3b09f4bedd92df6c8ef07b57d5568.pdf
[10]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
[11]Metzler, R.; Klafter, J.: The random walk’s guide to anomalous diffusion: a fractional dynamics approach, Physics reports 339, 1-77 (2000) · Zbl 0984.82032 · doi:10.1016/S0370-1573(00)00070-3
[12]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
[13]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
[14]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 · doi:emis:journals/EJQTDE/2010/201004.pdf
[15]Balachandran, K.; Kiruthika, S.; Trujillo, J. J.: Existence results for fractional impulsive integrodifferential equations in Banach spaces, Communications in nonlinear science and numerical simulation 16, 1970-1977 (2011) · Zbl 1221.34215 · doi:10.1016/j.cnsns.2010.08.005
[16]Hernández, E.; O’regan, D.; ; Balachandran, K.: On recent developments in the theory of abstract differential equations with fractional derivatives, Nonlinear analysis: theory, methods and applications 73, 3462-3471 (2010) · Zbl 1229.34004 · doi:10.1016/j.na.2010.07.035
[17]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
[18]He, J. H.: Some applications of nonlinear fractional differential equations and their approximations, Bulletin of science, technology and society 15, 86-90 (1999)
[19]Caputo, M.: Linear models of dissipation whose Q is almost frequency independent, part II, Geophysical journal of the royal astronomical society 13, 529-539 (1967)
[20]Li, M.; Chen, C.; Li, F. B.: On fractional powers of generators of fractional resolvent families, Journal of functional analysis 259, 2702-2726 (2010) · Zbl 1203.47021 · doi:10.1016/j.jfa.2010.07.007
[21]Prüss, J.: Evolutionary integral equations and applications, (1993)
[22]Smart, D. R.: Fixed point theorems, (1980)
[23]E.G. Bajlekova, Fractional Evolution Equations in Banach Spaces, Ph.D. Thesis, Eindhoven University of Technology, 2001. · Zbl 0989.34002