Omaba, Ejighikeme McSylvester (2018) On Space-Time Fractional Heat Type Non-Homogeneous Time-Fractional Poisson Equation. Journal of Advances in Mathematics and Computer Science, 28 (4). pp. 1-18. ISSN 24569968
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Abstract
Consider the following space-time fractional heat equation with Riemann-Liouville derivative of
non-homogeneous time-fractional Poisson process
211.PNG
where 221.PNGThe operator 231.PNG24.PNGwith 25.PNG(t) the Riemann-Liouville non-homogeneous fractional integral process, 26.PNGis the Caputo fractional derivative, 27.PNGis the generator of an isotropic stable process, 301.PNGis the fractional integral operator, and σ : R → R is Lipschitz continuous. The above time fractional stochastic heat type equations may be used to model sequence of catastrophic events 28.PNGfor some specific
rate functions were computed. Consequently, the growth moment bounds for the class of heat equation perturbed with the non-homogeneous fractional time Poisson process were given and we show that the solution grows exponentially for some small time interval 29.PNGand t0> 1; that is, the result establishes that the energy of the solution grows atleast as c4(t + t0) 18.PNG exp(c5t) and at most as c1t 19.PNGexp(c3t) for different conditions on the initialdata, where c1, c3, c4 and c5 are some positive constants depending on T. Existence and uniqueness result for the mild solution to the equation was given under linear growth condition on σ.
Item Type: | Article |
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Subjects: | Open Library Press > Mathematical Science |
Depositing User: | Unnamed user with email support@openlibrarypress.com |
Date Deposited: | 26 Apr 2023 08:32 |
Last Modified: | 16 Sep 2024 10:01 |
URI: | http://info.euro-archives.com/id/eprint/1140 |