Novel application of q-HAGTM to analyze Hilfer fractional differential equations in diabetic dynamics

Sangeeta Kumawat, Sanjay Bhatter, Bhamini Bhatia, Sunil Dutt Purohit, Haci Mehmet Baskonus and Daya Lal Suthar

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 238, issue C, 136-149

Abstract: Fractional calculus has emerged as a valuable tool for modeling complex dynamical systems due to its ability to represent the memory and hereditary characteristics. Among the various fractional operators, the Hilfer fractional derivative is particularly notable for its unique capability to interpolate between the Caputo and Riemann–Liouville derivatives, providing a versatile framework for fractional-order modeling. Although various numerical and analytical methods have been used to solve Hilfer fractional differential equations, the q-Homotopy analysis generalized transform method remains unexplored. In this study, we extend a glucose–insulin interaction model to a Hilfer fractional framework and apply this method to analyze its dynamics. The approach provides an effective solution technique, highlighting its potential for analyzing complex fractional-order biological systems. To establish the validity of our approach, we analyze the uniqueness and convergence of the obtained solutions. Numerical simulations and graphical representations illustrate the model’s behavior and confirm the method’s effectiveness. This study presents a novel application of the q-Homotopy analysis generalized transform method to Hilfer fractional equations. The results confirm the applicability and effectiveness of this method in obtaining reliable solutions. The findings contribute to the broader understanding of fractional-order modeling and demonstrate the potential of this approach for future research in mathematical modeling.

Keywords: Diabetes mellitus; q-Homotopy analysis method; Hilfer fractional operator; Generalized Laplace transformation (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475425001661
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:238:y:2025:i:c:p:136-149

DOI: 10.1016/j.matcom.2025.04.029

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().