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

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  • Omaba, McSylvester Ejighikeme

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.

Suggested Citation

  • Omaba, McSylvester Ejighikeme, 2021. "Growth moment, stability and asymptotic behaviours of solution to a class of time-fractal-fractional stochastic differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s096007792100312x
    DOI: 10.1016/j.chaos.2021.110958
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    References listed on IDEAS

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    1. Mijena, Jebessa B. & Nane, Erkan, 2015. "Space–time fractional stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3301-3326.
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    4. Jing Shao & Fanwei Meng, 2013. "Gronwall-Bellman Type Inequalities and Their Applications to Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, August.
    5. Nane, Erkan & Nwaeze, Eze R. & Omaba, McSylvester Ejighikeme, 2020. "Asymptotic behaviour of solution and non-existence of global solution to a class of conformable time-fractional stochastic equation," Statistics & Probability Letters, Elsevier, vol. 163(C).
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