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A Fractional-Order Bovine Babesiosis Epidemic Transmission Model With Nonsingular Mittag-Leffler Law

Author

Listed:
  • IBRAHIM SLIMANE

    (Faculty of Exact Sciences and Informatics, UMAB Abdelhamid Ibn Badis P. O. Box 227, University of Mostaganem, 27000 Mostaganem, Algeria)

  • JUAN J. NIETO

    (��Department of Statistics, Mathematical Analysis and Optimization, Galician Centre for Mathematical Research and Technology, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain)

  • SHABIR AHMAD

    (��Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan)

Abstract

In this paper, the model for bovine babesiosis epidemic transmission is analyzed using a fractional operator with a Mittag-Leffler kernel. The existence and uniqueness of the solution of the considered model is studied using real analysis. The Hyers–Ulam (HU) stability is investigated with the help of nonlinear functional analysis. The numerical results of the proposed model are deduced through the Adams–Bashforth technique, which is based on the two-step Lagrangian interpolation method. All results are simulated for a few fractional orders to observe the dynamics of the proposed model.

Suggested Citation

  • Ibrahim Slimane & Juan J. Nieto & Shabir Ahmad, 2023. "A Fractional-Order Bovine Babesiosis Epidemic Transmission Model With Nonsingular Mittag-Leffler Law," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-16.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:02:n:s0218348x23400339
    DOI: 10.1142/S0218348X23400339
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