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SUMMARY:A Fractional Stochastic Gompertz-Type Model Induced By Bernstein F
 unctions - Enrica Pirozzi (Università degli Studi di Napoli Federico II)
DTSTART:20220223T100000Z
DTEND:20220223T103000Z
UID:TALK167765@talks.cam.ac.uk
DESCRIPTION:In [1] we studied a class of linear fractional-integral stocha
 stic equations\, for which an existence and uniqueness result of a Gaussia
 n solution was proved. We used such kind of equations to construct fractio
 nal stochastic Gompertz models\, in such a way we included the fractional 
 Gompertz curves previously introduced in [3] and [4]. Then\, in [2]\, we f
 ocus on the construction of deterministic and stochastic extensions of the
  Gompertz curve by means of generalized fractional derivatives induced by 
 complete Bernstein functions. Specifically\, we introduce a class of linea
 r stochastic equations involving a generalized fractional integral and we 
 study the properties of the solutions. Deterministic generalized fractiona
 l Gompertz curves are introduced by means of Caputo-type generalized fract
 ional derivatives\, possibly with respect to other functions. A fractional
  rate process and a generalization of lognormal distrubution are also prov
 ided. (This is a joint work with Giacomo Ascione.)\nReferences[1] Ascione\
 , G.\; Pirozzi\, E. On the Construction of Some Fractional Stochastic Gomp
 ertz Models. Mathematics 8\, 60 (2020) https://doi.org/10.3390/math8010060
 [2] Ascione\, G.\; Pirozzi\, E. Generalized Fractional Calculus for Gomper
 tz-Type Models. Mathematics 2021\, 9\, 2140. https://doi.org/10.3390/math
 9172140[3] Bolton\, L.\; Cloot\, A.H.\; Schoombie\, S.W.\; Slabbert\, J.P.
  A proposed fractional-order Gompertz model and its application to tumour 
 growth data. Mathematical medicine and biology: a journal of the IMA 32\, 
 (2014)\, 187&ndash\;209.[4] Frunzo\, L.\; Garra\, R.\; Giusti\, A.\; Luong
 o\, V. Modeling biological systems with an improved fractional Gompertz la
 w. Communications in Nonlinear Science and Numerical Simulation\, 74\, (20
 19)\, 260&ndash\;267.
LOCATION:Seminar Room 1\, Newton Institute
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