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Abstract <p> Three-dimensional fractional integro-differential equations (3D-FIDEs) offer a robustmathematical framework with wide-ranging implications in image processing and physics. Thisstudy provides valuable insights into the existence, uniqueness and Hyers–Ulam stability ofsolutions to 3D-FIDEs using the Banach fixed point theorem, Arzela–Ascoli theorem andKrasnoselskii fixed point theorem. Moreover, this study successfully derives positive solutions aswell as maximal and minimal solutions for the problem. Furthermore, the paper includes a set ofnumerical examples to illustrate the theoretical findings and verify their validity. We also use thisIDE as an image-representation model for image processing applications and apply it to differenttypes of images. The results contribute to advancing knowledge in this area and lay thefoundation for further research and applications in fractional calculus.</p>

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Qualitative Studies of a Novel Three-Dimensional Fractional Integro-Differential Equation with Application in Image Representation

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • B. A. Miah,
  • M. Sen,
  • R. Murugan,
  • D. Gupta

摘要

Abstract

Three-dimensional fractional integro-differential equations (3D-FIDEs) offer a robustmathematical framework with wide-ranging implications in image processing and physics. Thisstudy provides valuable insights into the existence, uniqueness and Hyers–Ulam stability ofsolutions to 3D-FIDEs using the Banach fixed point theorem, Arzela–Ascoli theorem andKrasnoselskii fixed point theorem. Moreover, this study successfully derives positive solutions aswell as maximal and minimal solutions for the problem. Furthermore, the paper includes a set ofnumerical examples to illustrate the theoretical findings and verify their validity. We also use thisIDE as an image-representation model for image processing applications and apply it to differenttypes of images. The results contribute to advancing knowledge in this area and lay thefoundation for further research and applications in fractional calculus.