Skip to content
Research Article Open access CC BY 4.0

On Space-Time Fractional Heat Type Non-Homogeneous Time-Fractional Poisson Equation

Ejighikeme McSylvester Omaba

Journal of Advances in Mathematics and Computer Science · pp. 1–18 · Published 4 Sep 2018

10.9734/JAMCS/2018/33896

Abstract

Consider the following space-time fractional heat equation with Riemann-Liouville derivative of non-homogeneous time-fractional Poisson process where The operator with (t) the Riemann-Liouville non-homogeneous fractional integral process, is the Caputo fractional derivative, is the generator of an isotropic stable process, is 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 for 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 and t0> 1; that is, the result establishes that the energy of the solution grows atleast as c4(t + t0)  exp(c5t) and at most as c1t exp(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.

Caputo derivative energy moment bounds fractional heat kernel fractional Duhamel’s principle riemann-Liouville derivative riemann-Liouville integral process

References (12)

  1. 1 An introduction to stochastic partial differential equations [DOI]
  2. 2 Fractional Poisson Process [DOI]
  3. 3 On nonexistence of global solutions for some nonlinear integral equations [DOI]
  4. 4 Space–time fractional stochastic partial differential equations [DOI]
  5. 5 Some applications of the fractional Poisson probability distribution [DOI]
  6. 6 Beyond the Poisson renewal process: A tutorial survey [DOI]
  7. 7 A fractional counting process and its connection with the Poisson process [DOI]
  8. 8 Nonhomogeneous fractional Poisson processes [DOI]
  9. 9 On the integral of fractional Poisson processes [DOI]
  10. 10 On fractional Duhamel's principle and its applications [DOI]
  11. 11 Some Properties of a class of stochastic heat equations
  12. 12 Asymptotic properties of some space-time fractional stochastic equations [DOI]

Cited by 9

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

Asymptotic behaviour of solution and non-existence of global solution to a class of conformable time-fractional stochastic equation

Erkan Nane, Eze R. Nwaeze, McSylvester Ejighikeme Omaba · Statistics & Probability Letters · 2020

Moment Bound of Solution to a Class of Conformable Time-Fractional Stochastic Equation

McSylvester Ejighikeme Omaba, Eze R. Nwaeze · Fractal and Fractional · 2019

Atangana–Baleanu time-fractional stochastic integro-differential equation

McSylvester Ejighikeme Omaba, Cyril Dennis Enyi · Partial Differential Equations in Applied Mathematics · 2021

Showing 4 of 9 known citations — external sources report more than can currently be individually listed.

Related research

Article metrics

Real usage data collected on this platform.

7

Page views

0

PDF downloads

0

Outbound clicks

9

Citations

Views over time

Views by country

Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".

Traffic sources

Referring site, by host.

Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.