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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Existence, Uniqueness and Stability Results for Nonlinear Neutral Fractional Volterra-Fredholm Integro-Differential Equations

Discontinuity, Nonlinearity, and Complexity 12(2) (2023) 381--398 | DOI:10.5890/DNC.2023.06.011

$^1$ Department of Mathematics, Taiz University, Taiz P.O. Box 6803, Yemen

$^2$ Department of Mathematics, Hodeidah University, Al-Hudaydah, Yemen

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Abstract

In this paper, we established some new results concerning the existence and uniqueness of the solutions of nonlinear Volterra-Fredholm integro-differential equations of Caputo fractional order. These new results are obtained by using the Leray-Schauder nonlinear alternative, Krasnoselskii's and Banach fixed point theorems. In addition, we investigate generalized Ulam stability for this fractional system.

Acknowledgments

The authors would like to thank the anonymous referees and the handling editor for their careful reading and for relevant remarks/suggestions to improve the paper.

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