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New and Effective Oscillation Criteria for Solutions of a Class of First-Order Advanced Differential Equations Involving the Generalized Hausdorff Derivative

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  • Fatima Zohra Ladrani
  • Safa M. Mirgani
  • Amin Benaissa Cherif
  • Khaled Zennir

Abstract

In this paper, we investigate the oscillatory behavior of a class of first-order advanced differential equations involving the generalized Hausdorff derivative. By employing a recursive sequence method in combination with a Riccati transformation technique, we establish several new sufficient conditions that guaranty the oscillation of all solutions. The obtained criteria improve and extend existing oscillation results in two main directions. First, they are derived under weaker assumptions on the coefficient functions and deviating arguments. Second, they unify and generalize a number of previously known oscillation conditions for classical and fractional-type advanced differential equations as special cases. The effectiveness of the proposed approach is illustrated by showing that the new criteria apply to equations for which earlier results fail.

Suggested Citation

  • Fatima Zohra Ladrani & Safa M. Mirgani & Amin Benaissa Cherif & Khaled Zennir, 2026. "New and Effective Oscillation Criteria for Solutions of a Class of First-Order Advanced Differential Equations Involving the Generalized Hausdorff Derivative," Journal of Mathematics, Hindawi, vol. 2026, pages 1-11, May.
    • Handle: RePEc:hin:jjmath:7248349
    DOI: 10.1155/jom/7248349
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