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Stability region of fractional differential systems with Prabhakar derivative

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Abstract

This paper analyzes the stability of fractional differential equations with Prabhakar derivative, which is a generalization of the fractional differential equation with Caputo and Riemann-Liouville derivative. As a result, the sufficient condition for asymptotic stability has been obtained by studying the eigenvalues of system related matrix and the position of these eigenvalues in the complex plane. To show the application of the results a two-dimensional predator–prey model has been studied with Prabhakar derivative and the dynamic behavior has been extracted. Then, a numerical method along with its error has been presented for solving differential equations with Prabhakar derivative. The predator–prey model simulation has been conducted by using this numerical method.

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

    Javad Alidousti

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Alidousti, J. Stability region of fractional differential systems with Prabhakar derivative. J. Appl. Math. Comput. 62, 135–155 (2020). https://doi.org/10.1007/s12190-019-01277-8

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  • DOI: https://doi.org/10.1007/s12190-019-01277-8

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