Discrete fractional stochastic Grönwall inequalities arising in the numerical analysis of multi-term fractional order stochastic differential equations
Hendy A.S. Zaky M.A. Suragan D.
March 2022Elsevier B.V.
Mathematics and Computers in Simulation
2022#193269 - 279 pp.
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.
A priori estimate , Discrete stochastic fractional Grönwall inequalities , Interpolation schemes , Martingale , Multi-term time-fractional derivatives , Time delay
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Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg, 620002, Russian Federation
Department of Mathematics, Faculty of Science, Benha University, Benha, 13511, Egypt
Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Applied Mathematics, Physics Division, National Research Centre, Dokki, Cairo, 12622, Egypt
Department of Computational Mathematics and Computer Science
Department of Mathematics
Department of Mathematics
Department of Applied Mathematics
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