Study a class of Hilfer fractional stochastic integrodifferential equations with Poisson jumps |
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Authors: | P Balasubramaniam S Saravanakumar K Ratnavelu |
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Institution: | 1. Department of Mathematics, Gandhigram Rural Institute (Deemed to be University), Gandhigram, Tamil Nadu, India;2. balugru@gmail.com;4. Faculty of Science, Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia |
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Abstract: | AbstractIn this article, we derive the sufficient conditions for the existence of mild solutions of Hilfer fractional stochastic integrodifferential equations with nonlocal conditions and Poisson jumps in Hilbert spaces. Results will be obtained in the pth mean square sense by using the fractional calculus, semigroup theory and stochastic analysis techniques. The article generalizes many of the existing results in the literature in terms of (1) Riemann–Liouville and Caputo derivatives are the special cases. (2) In the sense of pth mean square norm. (3) Stochastic integrodifferential with nonlocal conditions and Poisson jumps. A numerical example is provided to validate the obtained theoretical results. |
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Keywords: | Hilfer fractional derivative stochastic fractional differential equations fixed point theorem mild solution nonlocal condition Poisson jumps |
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