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On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag–Leffler kernel

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Abstract

The purpose of this paper is to study the existence and uniqueness of the solution of nonlinear fractional differential equations with Mittag–Leffler nonsingular kernel. Two numerical methods to solve this problem are designed, and their stability and error estimates are investigated by discretizing the convolution integral and using the Grönwall’s inequality. Finally, the theoretical results are verified by using five illustrative examples.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey

    Dumitru Baleanu

  2. Institute of Space Sciences, P.O. Box MG-23, 76900, Magurele, Bucharest, Romania

    Dumitru Baleanu

  3. Department of Electrical Engineering, University of Bojnord, P.O. Box 94531-1339, Bojnord, Iran

    Amin Jajarmi

  4. Department of Mathematics, Sahand University of Technology, P.O. Box 51335-1996, Tabriz, Iran

    Mojtaba Hajipour

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  1. Dumitru Baleanu
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  2. Amin Jajarmi
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Correspondence to Dumitru Baleanu.

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Baleanu, D., Jajarmi, A. & Hajipour, M. On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag–Leffler kernel. Nonlinear Dyn 94, 397–414 (2018). https://doi.org/10.1007/s11071-018-4367-y

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  • DOI: https://doi.org/10.1007/s11071-018-4367-y

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