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Articles

Existence results for a class of impulsive neutral fractional stochastic integro-differential systems with state dependent delay

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Pages 865-892 | Received 29 Jul 2016, Accepted 10 Feb 2019, Published online: 03 Jun 2019

References

  • Evans, L. C. (2013). An Introduction to Stochastic Differential Equations. Berkeley, CA: University of California, Berkeley.
  • Gard, T. C. (1988). Introduction to Stochastic Differential Equations, Monographs and Textbooks in Pure and Applied Mathematics, 114. New York, NY: Dekker.
  • Mao, X. (2007). Stochastic Differential Equations and Applications. Chichester, UK: Horwood Publishing Limited.
  • Oksendal, B. (2002). Stochastic Differential Equations, 5th ed. Berlin, Germany: Springer.
  • Prato, G. D., Zabczyk, J. (1992). Stochastic Equations in Infinite Dimensions, Encyclopedia of Mathematics and Its Applications, 44. Cambridge, UK: Cambridge University Press.
  • Hernandez, E., O’Regan, D. (2013). On a new class of abstract impulsive differential equations. Proc. Amer. Math. Soc. 141:1641–1649.
  • Pierri, M., O'Regan, D., Rolnik, V. (2013). Existence of solutions for semi-linear abstract differential equations with not instantaneous impulses. Appl. Math. Comput. 219:6743–6749. DOI: 10.1016/j.amc.2012.12.084.
  • Hilfer, R. (2000). Applications of Fractional Calculus in Physics. Singapore, Singapore: World Scientific.
  • Kilbas, A. A., Srivastava, H. M., Trujillo, J. J. (2006). Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204. Amsterdam, The Netherlands: Elsevier Science B.V.
  • Miller, K. S., Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, a Wiley-Interscience Publication. New York, NY: John Wiley and Sons, Inc.
  • Podlubny, I. (1999). Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Mathematics in Science and Engineering, 198. San Diego, CA: Academic Press, Inc.
  • Balasubramaniam, P., Vinayagam, D. (2005). Existence of solutions of nonlinear neutral stochastic differential inclusions in a Hilbert space. Stochastic Anal. Appl. 23(1):137–151. DOI: 10.1081/SAP-200044463.
  • Anguraj, A., Vinodkumar, A. (2009). Existence, uniqueness and stability results of impulsive stochastic semilinear neutral functional differential equations with infinite delays. Electron. J. Qual. Theory Differ. Equ. 67:13. DOI: 10.14232/ejqtde.2009.1.67.
  • Balasubramaniam, P., Park, J. Y., Kumar, A. V. A. (2009). Existence of solutions of semilinear neutral stochastic functional differential equations with nonlocal conditions. Nonlinear Anal. 71(3–4):1049–1058. DOI: 10.1016/j.na.2008.11.032.
  • Cui, J., Yan, L. (2011). Existence results for fractional neutral stochastic integrodifferential equations with infinite delay. J. Phys. A: Math. Theory 44:1–16.
  • Hu, L., Ren, Y. (2010). Existence results for impulsive neutral stochastic functional integro-differential equations with infinite delays. Acta Appl. Math. 111(3):303–317. DOI: 10.1007/s10440-009-9546-x.
  • Chen, P., Li, Y. (2015). Nonlocal Cauchy problem for fractional stochastic evolution equations in Hilbert spaces. Collect. Math. 66(1):63–76. DOI: 10.1007/s13348-014-0106-y.
  • Pandey, D. N., Das, S., Sukavanam, N. (2014). Existence of solution for a second-order neutral differential equation with state dependent delay and non-instantaneous impulses. Int. J. Nonlinear Sci. 18:145–155.
  • Yan, Z. (2016). On a new class of impulsive stochastic partial neutral integro-differential equations. Appl. Anal. 95(9):1891–1918. DOI: 10.1080/00036811.2015.1076568.
  • Gautam, G. R., Dabas, J. (2015). Mild solutions for class of neutral fractional functional differential equations with not instantaneous impulses. Appl. Math. Comput. 259:480–489. DOI: 10.1016/j.amc.2015.02.069.
  • Suganya, S., Kalamani, P., Arjunan, M. M. (2016). Existence of a class of fractional neutral integro-differential systems with state dependent delay in Banach spaces. Comp. Math. Appl. (In Press). DOI: 10.1016/j.camwa.2016.01.016.
  • Aiello, W. G., Freedman, H. I., Wu, J. (1992). Analysis of a model representing stage-structured population growth with state-dependent time delay. SIAM J. Appl. Math. 52(3):855–869. DOI: 10.1137/0152048.
  • Benchohra, M., Litimein, S., N'Guerekata, G. (2013). On fractional integro-differential inclusions with state-dependent delay in Banach spaces. Appl. Anal. 92(2):335–350. DOI: 10.1080/00036811.2011.616496.
  • Cao, Y., Fan, J., Gard, T. C. (1992). The effects of state-dependent time delay on a stage-structured population growth model. Nonlinear Anal. 19(2):95–105. DOI: 10.1016/0362-546X(92)90113-S.
  • dos Santos, J. P. C., Mallika Arjunan, M., Cuevas, C. (2011). Existence results for fractional neutral integro-differential equations with state-dependent delay. Comp. Math. Appl. 62(3):1275–1283. DOI: 10.1016/j.camwa.2011.03.048.
  • Hartung, F., Turi, J. (1997). Identification of parameters in delay equations with state-dependent delays. Nonlinear Anal. 29(11):1303–1318. DOI: 10.1016/S0362-546X(96)00100-9.
  • Hernandez, E., Prokopczyk, A., Ladeira, L. (2006). A note on partial functional differential equations with state-dependent delay. Nonlinear Anal. Real World Appl. 7:510–519. DOI: 10.1016/j.nonrwa.2005.03.014.
  • Pazy, A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44. New York, NY: Springer.
  • Hale, J. K., Kato, J. (1978). Phase space for retarded equations with infinite delay. Funkcial. Ekvac 21:11–41.
  • Hino, Y., Murakami, S., Naito, T. (1991). Functional Differential Equations with Infinite Delay, Lecture Notes in Mathematics. Berlin: Springer-Verlag.
  • Zhou, Y., Jiao, F. (2010). Existence of mild solutions for fractional neutral evolution equations. Comput. Math. Appl. 59(3):1063–1077. DOI: 10.1016/j.camwa.2009.06.026.
  • Banas, J., Goebel, K. (1980). Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics, 60. New York: Marcel Dekker, Inc.
  • Heinz, H. (1983). On the behaviour of measures of noncompactness with respect to differentiation and integration of vector valued functions. Nonlinear Anal. 7(12):1351–1371. DOI: 10.1016/0362-546X(83)90006-8.

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