Applied Research Advances

Vol. 2 No. 1 (2026): Applied Research Advances
Articles

An Introduction of the Mellin Transformation under Interval Uncertainty

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  • Musaraf Hossain,
  • Mostafijur Rahaman,
  • Shariful Alam
Musaraf Hossain
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, India
Mostafijur Rahaman
Department of Mathematics and Statistics, School of Applied Sciences and Humanities, Vignan’s Foundation for Science, Technology and Research, Guntur, Andhra Pradesh, India
Shariful Alam
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, India

Published 2026-06-18

Keywords

  • Melin Transformation,
  • Scaling Property,
  • Generalized Hukuhara Derivative,
  • Applied Computation,
  • Interval Valued Function,
  • Signal Processing
    • ...More
    Less

Copyright (c) 2026 Musaraf Hossain, Mostafijur Rahaman, Shariful Alam (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Hossain, M., Rahaman, M., & Alam, S. . (2026). An Introduction of the Mellin Transformation under Interval Uncertainty. Applied Research Advances, 2(1), 169-178. https://doi.org/10.65069/ara21202612
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Abstract

Mellin transformation has potential applications in signal processing, quantum mechanics, and numerous domains of knowledge. Data collection and its interpretations must go through impreciseness in almost every real field of decision-making or modelling. In this paper, we contribute an alternative approach for the Mellin transformation under imprecision. The interval-valued Mellin transformation is introduced in this paper. We discuss the linearity, scaling, and sifting properties of the interval-valued transformation. Also, the Mellin transformation of the generalized Hukuhara derivative of the interval-valued function is addressed. One possible application of interval-valued Mellin transformation to solve an uncertain Euler differential equation is manifested, and several more consequent applications are hinted.

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