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Local and Global Existence of Mild Solution for Impulsive Fractional Stochastic Differential Equations

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Abstract

In this paper, the local and global existence of mild solutions are studied for impulsive fractional semilinear stochastic differential equation with nonlocal condition in a Hilbert space. The results are obtained by employing fixed-point technique and solution operator. In many existence results for stochastic fractional differential systems, the value of \(\alpha \) is restricted to \(\frac{1}{2} < \alpha \le 1;\) the aim of this manuscript is to extend the results which are valid for all values of \(\alpha \in (0,\,1).\) An example is provided to illustrate the obtained theoretical results.

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Acknowledgments

The work of authors are supported by Council of Scientific and Industrial Research, Extramural Research Division, Pusa, New Delhi, India under the Grant No. 25(0217)/13/EMR-II and UMRG Grant Account No. RG099/10AFR.

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Authors and Affiliations

  1. Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, 624 302, Tamil Nadu, India

    P. Balasubramaniam & P. Tamilalagan

  2. Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia

    N. Kumaresan & K. Ratnavelu

Authors
  1. P. Balasubramaniam
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  2. N. Kumaresan
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  3. K. Ratnavelu
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  4. P. Tamilalagan
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Correspondence to P. Balasubramaniam.

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Communicated by Norhashidah M. Ali.

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Balasubramaniam, P., Kumaresan, N., Ratnavelu, K. et al. Local and Global Existence of Mild Solution for Impulsive Fractional Stochastic Differential Equations. Bull. Malays. Math. Sci. Soc. 38, 867–884 (2015). https://doi.org/10.1007/s40840-014-0054-4

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  • DOI: https://doi.org/10.1007/s40840-014-0054-4

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