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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

Topological Degree Method for Stochastic Pantograph Differential Equation with Hilfer Fractional Derivative Involving Non-instantaneous Impulses

Discontinuity, Nonlinearity, and Complexity 15(3) (2026) 315--330 | DOI:10.5890/DNC.2026.09.002

Ayoub Louakar$^{1}$, Devaraj Vivek$^{2}$, Ahmed Kajouni$^{1}$, Khalid Hilal$^{1}$

$^{1}$ Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco

$^{2}$ Department of Mathematics, PSG College of Arts and Science, Coimbatore-641014, India

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Abstract

This study examines a class of fractional stochastic pantograph differential equations involving the Hilfer fractional derivative and non-instantaneous impulses. The existence of solutions is established using topological degree theory, while Banach's contraction principle is employed to demonstrate uniqueness. Additionally, an illustrative example and graphical analysis are provided to validate the findings.

Acknowledgments

The authors are thankful to the referee's thoughtful comments on the manuscript, which helped to improve it.

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