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OSCILLATION ANALYSIS OF CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS WITH ADVANCED AND DELAY ARGUMENTS VIA A MONOTONICITY APPROACH

AUTHORS:
Jyoti Thenge-Mashale
Vishal Koli
Manasi Patil
Mentor
Affiliation
DOI: 10.55041/ijsmt.v2i7.052
CC BY 4.0 License:
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Abstract
In this paper , we investigate the oscillatory behavior of a class of Caputo fractional differen-tial equations involving both advanced and delayed arguments.By establishing novel monotonicity proper-ties of eventually positive solutions,we derive improved sufficient conditions for the nonexistence of positive monotone solutions.New auxiliary functions are introduced to obtain unified monotonicity results without imposing restrictive assumptions on the coefficient functions,thereby extending and strengthening several existing oscillation criteria.The developed approach yields sharper oscillation conditions for both advanced and ratarded fractional differential equations and is further extended to equations containing simultaneously advanced and delayed arguments.Several illustrative examples are presented to demonstrate the effective-ness of the proposed criteria and to highlight the significant improvement over previously known results.The obtained results contribute to the qualitative theory of fractional differential equations and provide a useful framework for the anaiysis of oscillatory behavior in fractional dynamical systems with deviating arguments.
Keywords
Caputo fractional derivative Fractional differential equations Oscillation Advanced argument Delay differential equation Monotonicity Qualitative analysis.
Article Information
PUBLICATION DETAILS
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Double-Blind Peer Review
License:
CC BY-NC 4.0
Volume/Issue:
Volume 02, Issue 7
Review Rounds:
2
Article Type:
Research Article
Publication Date:
Jul 10 2026
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Thenge-Mashale, J., Koli, V. & Patil, M. (2026). Oscillation Analysis of Caputo Fractional Differential Equations with Advanced and Delay Arguments via a Monotonicity Approach. International Journal of Science, Strategic Management and Technology, 02(7). https://doi.org/10.55041/ijsmt.v2i7.052

Thenge-Mashale, Jyoti, et al.. "Oscillation Analysis of Caputo Fractional Differential Equations with Advanced and Delay Arguments via a Monotonicity Approach." International Journal of Science, Strategic Management and Technology, vol. 02, no. 7, 2026, pp. . doi:https://doi.org/10.55041/ijsmt.v2i7.052.

Thenge-Mashale, Jyoti,Vishal Koli, and Manasi Patil. "Oscillation Analysis of Caputo Fractional Differential Equations with Advanced and Delay Arguments via a Monotonicity Approach." International Journal of Science, Strategic Management and Technology 02, no. 7 (2026). https://doi.org/https://doi.org/10.55041/ijsmt.v2i7.052.

References

  1. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.

  2. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.

  3. Diethelm, The Analysis of Fractional Differential Equations, Springer, Berlin, 2010.

  4. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, New York, 1993.

  5. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equa-tions, John Wiley & Sons, New York, 1993.

  6. Lakshmikantham, S. Leela and J. Vasundhara Devi, Theory of Fractional Dynamic Systems, Cam-bridge Scientific Publishers, 2009.

  7. P. Agarwal, S. R. Grace and D. O’Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, 2000.

  8. R. Grace, R. P. Agarwal, P. J. Y. Wong and A. Zafer, On the oscillation of fractional differential equations, Fractional Calculus and Applied Analysis, 13(2010), 225–236.

  9. X. Chen, J. S. Yu and P. Li, Oscillation criteria for nonlinear fractional differential equations with damping, Electronic Journal of Differential Equations, 2013(2013), No. 59, 1–10.

  10. Baleanu, K. Diethelm, E. Scalas and J. J. Trujillo, Fractional Calculus: Models and Numerical Methods, World Scientific, Singapore, 2012.

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This article has undergone plagiarism screening and double-blind peer review. Editorial policies have been followed. Authors retain copyright under CC BY-NC 4.0 license. The research complies with ethical standards and institutional guidelines.
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