On a new class of impulsive stochastic partial neutral integro-differential equations

References

• Benchohra M, Henderson J, Ntouyas SK. Impulsive differential equations and inclusions. New York (NY): Hindawi Publishing Corporation; 2006.
   Google Scholar
• Hernández E, Rabello M, Henríquez H. Existence of solutions for impulsive partial neutral functional differential equations. J. Math. Anal. Appl. 2007;331:1135–1158.
   Web of Science ®Google Scholar
• Hernández E, McKibben M, Henríquez HR. Existence results for partial neutral functional differential equations with state-dependent delay. Math. Comput. Model. 2009;49:1260–1267.
   Web of Science ®Google Scholar
• Mao X. Stochastic differential equations and their applications. Chichester: Horwood Publishing Ltd.; 1997.
   Google Scholar
• Ren Y, Bi Q, Sakthivel R. Stochastic functional differential equations with infinite delay driven by G-Brownian motion. Math. Methods Appl. Sci. 2013;36:1746–1759.
   Web of Science ®Google Scholar
• Cui J, Yan L. Existence result for fractional neutral stochastic integro-differential equations with infinite delay. J. Phys. A. 2011;44:1–18.
   Google Scholar
• Revathi P, Sakthivel R, Song D-Y, Ren Y, Zhang P. Existence and stability results for second-order stochastic equations driven by fractional Brownian motion. Transp. Theory Stat. Phys. 2013;42:299–317.
   Web of Science ®Google Scholar
• Sakthivel R, Luo J. Asymptotic stability of impulsive stochastic partial differential equations with infinite delays. J. Math. Anal. Appl. 2009;356:1–6.
   Web of Science ®Google Scholar
• Sakthivel R, Ren Y, Mahmudov NI. Approximate controllability of second-order stochastic differential equations with impulsive effects. Modern Phys. Lett. B. 2010;24:1559–1572.
   Web of Science ®Google Scholar
• Anguraj A, Vinodkumar A. Existence, uniqueness and stability results of impulsive stochastic semilinear neutral functional differential equations with infinite delays. E. J. Qual. Theory Diff. Equ. 2009;67:1–13.
   Google Scholar
• Sakthivel R, Revathi P, Ren Y. Existence of solutions for nonlinear fractional stochastic differential equations. Nonlinear Anal. 2013;81:70–86.
   Web of Science ®Google Scholar
• Lin A, Ren Y, Xia N. On neutral impulsive stochastic integro-differential equations with infinite delays via fractional operators. Math. Comput. Model. 2010;51:413–424.
   Web of Science ®Google Scholar
• Hu L, Ren Y. Existence results for impulsive neutral stochastic functional integro-differential equations with infinite delays. Acta Appl. Math. 2010;111:303–317.
   Web of Science ®Google Scholar
• Yan Z, Yan X. Existence of solutions for impulsive partial stochastic neutral integrodifferential equations with state-dependent delay. Collect. Math. 2013;64:235–250.
   Web of Science ®Google Scholar
• Yan Z, Zhang H. Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with state-dependent delay. Electron. J. Differ. Equ. 2013;206:1–29.
   Google Scholar
• Zang Y, Li J. Approximate controllability of fractional impulsive neutral stochastic differential equations with nonlocal conditions. Bound. Value Probl. 2013;193:1–14.
   Google Scholar
• Hernández E. Donal O’Regan, On a new class of abstract impulsive differential equations. Proc. Amer. Math. Soc. 2013;141:1641–1649.
   Web of Science ®Google Scholar
• Pierri M, O’Regan D, Rolnik V. Existence of solutions for semi-linear abstract differential equations with not instantaneous impulses. Appl. Math. Comput. 2013;219:6743–6749.
   Web of Science ®Google Scholar
• Pandey DN, Das S, Sukavanam N. Existence of solution for a second-order neutral differential equation with state dependent delay and non-instantaneous impulses. Int. J. Nonlinear Sci. 2014;18:145–155.
   Google Scholar
• Gautam GR, Dabas J. Mild solution for fractional functional integro-differential equation with not instantaneous impulse. Malaya J. Mat. 2014;2:428–437.
   Google Scholar
• Yan Z, Lu F. Existence results for a new class of fractional impulsive partial neutral stochastic integro-differential equations with infinite delay. J. Appl. Anal. Comput. 2015;5:329–346.
   Web of Science ®Google Scholar
• Yu X, Wang J. Periodic boundary value problems for nonlinear impulsive evolution equations on Banach spaces. Commun. Nonlinear Sci. Numer. Simul. 2015;22:980–989.
   Web of Science ®Google Scholar
• Grimmer R, Pritchard AJ. Analytic resolvent operators for integral equations in a Banach space. J. Differ. Equ. 1983;50:234–259.
   Web of Science ®Google Scholar
• Grimmer R. Resolvent operators for integral equations in a Banach space. Trans. Amer. Math. Soc. 1982;273:333–349.
   Web of Science ®Google Scholar
• Pazy A. Semigroups of linear operators and applications to partial differential equations. New York (NY): Springer; 1983.
   Google Scholar
• Hale JK, Kato J. Phase spaces for retarded equations with infinite delay. Funkcial. Ekvac. 1978;21:11–41.
   Google Scholar
• Banas J, Goebel K. Measure of noncompactness in Banach space. Lecture notes in pure and applied mathematics. New York (NY): Dekker; 1980.
   Google Scholar
• Rogovchenko YV. Nonlinear impulse evolution systems and applications to population models. J. Math. Anal. Appl. 1997;207:300–315.
   Web of Science ®Google Scholar
• Da Prato G, Zabczyk J. Stochastic equations in infinite dimensions. Cambridge: Cambridge University Press; 1992.
   Google Scholar
• Agarwal R, Meehan M, O’Regan D. Fixed point theory and applications. Cambridge tracts in mathematics. New York (NY): Cambridge University Press; 2001. p.178–179.
   Google Scholar
• Bajlekova E. Fractional evolution equations in Banach spaces [PhD thesis]. Eindhoven: Eindhoven University of Technology; 2001.
   Google Scholar
• Hino Y, Murakami S, Naito T. Functional-differential equations with infinite delay. Vol. 1473, Lecture notes in mathematics. Berlin: Springer-Verlag; 1991.
   Google Scholar