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Stability and dynamics of neutral and integro-differential regularized Prabhakar fractional differential systems

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Abstract

In this work, we investigate the asymptotic stability analysis for two classes of nonlinear fractional systems with the regularized Prabhakar derivative. The stability analysis of the neutral and integro-differential nonlinear fractional systems are studied by assessing the eigenvalues of associated matrix and applying conditions on the nonlinear part of these types of systems. We use a numerical method to solve the fractional differential equations with the regularized Prabhakar fractional derivative. We further present the numerical simulations on several test cases to examine and reveal the complex dynamics of the analytical obtained results.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran

    Shiva Eshaghi, Reza Khoshsiar Ghaziani & Alireza Ansari

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  1. Shiva Eshaghi
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  2. Reza Khoshsiar Ghaziani
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  3. Alireza Ansari
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Correspondence to Alireza Ansari.

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Communicated by José Tenreiro Machado.

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Eshaghi, S., Ghaziani, R.K. & Ansari, A. Stability and dynamics of neutral and integro-differential regularized Prabhakar fractional differential systems. Comp. Appl. Math. 39, 250 (2020). https://doi.org/10.1007/s40314-020-01296-3

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  • DOI: https://doi.org/10.1007/s40314-020-01296-3

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