Discrete fractional stochastic Grönwall inequalities arising in the numerical analysis of multi-term fractional order stochastic differential equations

Ahmed S. Hendy, Mahmoud A. Zaky and Durvudkhan Suragan

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 193, issue C, 269-279

Abstract: This paper is devoted to the rigorous derivation of some discrete versions of stochastic Grönwall inequalities involving a martingale, which are commonly used in the numerical analysis of multi-term stochastic time-fractional diffusion equations. A Grönwall lemma is also established to deal with the numerical analysis of multi-term stochastic fractional diffusion equations with delay. The proofs of the established inequalities are based on a corresponding deterministic version of the discrete fractional Grönwall lemma in case of smooth solutions and an inequality bounding the supremum in terms of the infimum for discrete time martingales. A numerical application is introduced finally in which the constructed inequalities are handled to derive a priori estimates for a discrete fractional stochastic model.

Keywords: Discrete stochastic fractional Grönwall inequalities; Martingale; Interpolation schemes; A priori estimate; Multi-term time-fractional derivatives; Time delay (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:193:y:2022:i:c:p:269-279

DOI: 10.1016/j.matcom.2021.10.013

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