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Discontinuity, Nonlinearity, and Complexity 15(4) (2026) 639--653 | DOI:10.5890/DNC.2026.12.012

Svetlin G. Georgiev$^{1}$, Ranis N. Ibragimov$^{2}$, Aba Anokye Appiaa$^{2}$

$^{1}$ Department of Mathematics, Sorbonne University, Paris, France

$^{2}$ Department of Mathematics, Hampton University, Hampton, VA 23668, USA

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Abstract

The class of Burgers equations is examined within the context of time scales that incorporate forward jump operators. The study establishes the existence of at least one solution, as well as a minimum of two nonnegative solutions and at least three nonnegative solutions. For this aim we use some recent fixed-point theorems. We construct two operators so that any fixed-point of their sum is a solution of the initial value problem (IVP) for the considered class of Burgers equations. The results of this paper are provided with a suitable example to illustrate the main findings.

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