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Approximation of Solutions to Stochastic Neutral Fractional Integro-Differential Equation with Nonlocal Conditions

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Abstract

In this paper, we study a stochastic neutral fractional integro-differential equation with nonlocal conditions in separable Hilbert spaces. We obtain an associated integral equation and then, consider a sequence of approximate integral equations. We used the semigroup theory of linear operators and stochastic version of Banach fixed point theorem to study the existence and uniqueness of the mild solution for every approximate integral equation. Next, we show the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. Moreover, the Faedo–Galerkin approximation of solution is established. In the last, an example is provided to illustrate the applications of the abstract results.

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Acknowledgments

The authors would like to thank the editor and the reviewers for their valuable comments and suggestions. The work of the first author is supported by the “Ministry of Human Resource and Development, India under Grant Number: MHR-02-23-200-44”.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Renu Chaudhary & Dwijendra N Pandey

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  1. Renu Chaudhary
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  2. Dwijendra N Pandey
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Correspondence to Renu Chaudhary.

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Chaudhary, R., Pandey, D.N. Approximation of Solutions to Stochastic Neutral Fractional Integro-Differential Equation with Nonlocal Conditions. Int. J. Appl. Comput. Math 3, 1203–1223 (2017). https://doi.org/10.1007/s40819-016-0171-x

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