Growth moment, stability and asymptotic behaviours of solution to a class of time-fractal-fractional stochastic differential equation

McSylvester Ejighikeme Omaba

Chaos, Solitons & Fractals, 2021, vol. 147, issue C

Abstract: We investigate a class of time-fractal-fractional Stochastic differential equation with the Atangana’s fractal-fractional differential operator in Caputo sense with power law type kernel. The upper growth bound of the random solution to the equation is estimated, and the result shows that the second moment of the solution grows exponentially at most at a precise rate. The existence and uniqueness result of the solution is also established via Banach fixed point theorem and contraction principle. We also show that the solution exhibits some long time asymptotic behaviours and some form of mean square exponential stability property.

Keywords: Fractal-fractional operators; Moment estimates; Growth bounds; Existence and uniqueness (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:147:y:2021:i:c:s096007792100312x

DOI: 10.1016/j.chaos.2021.110958

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