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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Analyzing Integral Equations through the Application of Fractional Calculus and Incomplete $aleph$-Function

Journal of Applied Nonlinear Dynamics 15(2) (2026) 313--324 | DOI:10.5890/JAND.2026.06.004

Manisha Meena$^{1,2}$, Mridula Purohit$^1$

$^{1}$ Department of Mathematics, Vivekananda Global University Jaipur, India

$^{2}$ Department of Mathematics, Motilal Nehru College, (University of Delhi) Delhi, India

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Abstract

This article explores a Fredholm-type integral equation featuring an incomplete $\aleph$-function in its kernel, with implications for solving real-world problems representing diverse physical phenomena. Employing fractional calculus and Mellin transform principles, we address an integral problem involving the incomplete $\aleph$-function. The Mellin transform and fractional calculus are subsequently applied to analyze an integral equation using the incomplete $\aleph$-function. Various significant exceptional cases have been identified and scrutinized. The general insights from this article may lead to the formulation of new integral equations and solutions, contributing to the resolution of practical challenges.

Acknowledgments

The authors express their sincere thanks to the editor and reviewers for their fruitful comments and suggestions that improved the quality of the manuscript.

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