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

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

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)269-279
Number of pages11
JournalMathematics and Computers in Simulation
Volume193
DOIs
Publication statusPublished - Mar 2022

Keywords

  • A priori estimate
  • Discrete stochastic fractional Grönwall inequalities
  • Interpolation schemes
  • Martingale
  • Multi-term time-fractional derivatives
  • Time delay

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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