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Analysis Sequential Fractional Differences And Related Monotonicity Results

Author

Listed:
  • PSHTIWAN OTHMAN MOHAMMED

    (Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq†Research and Development Center, University of Sulaimani, Sulaymaniyah 46001, Iraq)

  • CARLOS LIZAMA

    (��Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencias, Universidad de Santiago de Chile, Las Sophoras 173, Estación Central, Santiago, Chile)

  • EMAN AL-SARAIRAH

    (�Department of Mathematics, Khalifa University of Science and Technology, P. O. Box 127788, Abu Dhabi, United Arab Emirates¶Department of Mathematics, Al-Hussein Bin Talal University, P. O. Box 20, Ma’an 71111, Jordan)

  • JUAN L. G. GUIRAO

    (��Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina 30203-Cartagena, Spain)

  • NEJMEDDINE CHORFI

    (*Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia)

  • MIGUEL VIVAS-CORTEZ

    (��†Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Av. 12 de octubre 1076 y Roca, Apartado Postal 17-01-2184, Sede Quito, Ecuador)

Abstract

This paper employs the monotonicity analysis for non-negativity to derive a class of sequential fractional backward differences of Riemann–Liouville type a+1RL∇ν aRL∇αu (t) based on a certain subspace in the parameter space (0, 1) × (0, 1). Auxiliary and restriction conditions are included in the monotonicity results obtained in this paper and they confirm the monotonicity of the function on {a + 2,a + 3,…}. A non-monotonicity result is also established based on the main conditions together with further dual conditions, and this confirms that the main theorem is almost sharp. Furthermore, we recast the dual conditions in a sing condition, and then we represent the sharpness result in a new corollary. Finally, numerical results via MATLAB software are used to illustrate the main mathematical results for some special cases.

Suggested Citation

  • Pshtiwan Othman Mohammed & Carlos Lizama & Eman Al-Sarairah & Juan L. G. Guirao & Nejmeddine Chorfi & Miguel Vivas-Cortez, 2024. "Analysis Sequential Fractional Differences And Related Monotonicity Results," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(07n08), pages 1-10.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:07n08:n:s0218348x24400371
    DOI: 10.1142/S0218348X24400371
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