Computational and Applied Mathematics

, Volume 37, Issue 5, pp 6433–6447 | Cite as

Numerical simulation of fractional-order dynamical systems in noisy environments

  • Zeinab Salamat Mostaghim
  • Behrouz Parsa MoghaddamEmail author
  • Hossein Samimi Haghgozar


In this paper, the fully discrete scheme is proposed based on the Simpson’s quadrature formula to approximate fractional-order integrals for noisy signals. This strategy is extended to simulate the response of fractional-order differential systems in noisy environments. The proposed technique is considered in determining statistical indicators for noisy signals in fractional electrical networks with white noise-influenced potential sources.


Fractional calculus Stochastic calculus Fractional differential equations Fractional electrical circuits Computational method 

List of symbols


\({{\text {Inductance}, \ (H)}}\)


\({{\text {Resistance}, \ ({\varOmega })}}\)


\({{\text {Inductor current function}, \ (A)}}\)


\({{\text {Potential source function}, \ (V)}}\)

\(\alpha \) and \(\beta \)

\(\text {Amplitude of the noise parameters}\)

\(\omega _1(t)\) and \(\omega _2(t)\)

\(\text {Two uncorrelated one-dimensional standard Wiener processes}\)

\({\vartheta (t)}\)

\(\text {Gaussian white noise function}\)

Mathematics Subject Classification

26A33 34A08 62L20 60H35 


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018

Authors and Affiliations

  • Zeinab Salamat Mostaghim
    • 1
  • Behrouz Parsa Moghaddam
    • 1
    Email author
  • Hossein Samimi Haghgozar
    • 2
  1. 1.Department of Mathematics, Lahijan BranchIslamic Azad UniversityLahijanIran
  2. 2.Department of Statistics, Faculty of Mathematical SciencesUniversity of GuilanRashtIran

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