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Discontinuity, Nonlinearity, and Complexity 12(2) (2023) 399--410 | DOI:10.5890/DNC.2023.06.012

$^1$ Mathematics Department, Faculty of Science, University of Ha'il, Kingdom of Saudi Arabia

$^2$ Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, Algeria

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Abstract

In this paper, we consider nonlinear neutral q-fractional difference equations which have important applications in many domains of life sciences. By using the Krasnoselskii fixed point theorem, sufficient conditions for the existence of solutions are established, also the uniqueness of solutions is given. As an application of the main theorems, we provide the existence and uniqueness of the discrete $q$-fractional Lotka-Volterra model of neutral type. Our main theorems are important results because are extend and generalize the results in the literature.

Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments and good advices.

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