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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

An Approach on Nonlocal Neutral Impulsive Fractional Differential Equation of Sobolev Type via Poisson Jumps

Discontinuity, Nonlinearity, and Complexity 15(2) (2026) 293--308 | DOI:10.5890/DNC.2026.06.012

M. Manjula$^1$, K. Kaliraj$^1$, J. Vernold Vivin$^2$

$^1$ Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, Tamil Nadu, India

$^2$ Department of Mathematics, Anna University Regional Campus Coimbatore, Maruthamalai Road, Coimbatore 641 046, Tamil Nadu, India

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Abstract

The present work establishes the neutral fractional impulsive differential equation (NFIDE). The fixed-point method and probability density function (PDF) are used to demonstrate the existence and uniqueness of solutions through nonlocal conditions. We show that the approximation integral equation solutions are convergent to the corresponding integral equation. The convergence is shown using the fractional theory. We then obtain an original solution via the Faedo-Galerkin approximation techniques. Additionally, we provide an application for assessing empirical outcomes.

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