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Mittag–Leffler Fractional Stochastic Integrals and Processes with Applications

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  • Enrica Pirozzi

    (Dipartimento di Matematica e Fisica, Università della Campania “Luigi Vanvitelli”, 81100 Caserta, Italy)

Abstract

We study Mittag–Leffler (ML) fractional integrals involved in the solution processes of a system of coupled fractional stochastic differential equations. We introduce the ML fractional stochastic process as a ML fractional stochastic integral with respect to a standard Brownian motion. We provide some representation formulas of solution processes in terms of Mittag–Leffler fractional integrals and processes. Computable expressions of the mean functions and of the covariances of such processes are specifically given. The application in neuronal modeling is provided, and all involved functions and processes are specifically determined. Numerical evaluations are carried out and some results are shown and discussed.

Suggested Citation

  • Enrica Pirozzi, 2024. "Mittag–Leffler Fractional Stochastic Integrals and Processes with Applications," Mathematics, MDPI, vol. 12(19), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3094-:d:1491412
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    References listed on IDEAS

    as
    1. Giacomo Ascione & Bruno Toaldo, 2019. "A Semi-Markov Leaky Integrate-and-Fire Model," Mathematics, MDPI, vol. 7(11), pages 1-24, October.
    2. Bazzani, Armando & Bassi, Gabriele & Turchetti, Giorgio, 2003. "Diffusion and memory effects for stochastic processes and fractional Langevin equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 530-550.
    3. Anh, P.T. & Doan, T.S. & Huong, P.T., 2019. "A variation of constant formula for Caputo fractional stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 351-358.
    4. Tuckwell, Henry C., 2006. "Spatial neuron model with two-parameter Ornstein–Uhlenbeck input current," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(2), pages 495-510.
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