Fractional-order modeling and numerical analysis of double intermediate enzymatic reaction model using generalized Euler method

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 24 آبان 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.94700.1692

نویسندگان

Koushick B¹؛ Vignesh Raju R²؛ Anbazhagan N¹؛ Jeeva N^{* 3، 4}

¹Department of Mathematics, Alagappa University, Karaikudi 630003, Tamil Nadu, India.

²PG and Research Department of Mathematics, Vidhyaa Giri College of Arts and Science, Puduvayal 630108, Tamil Nadu, India.

³Department of Mathematics, K.S. Rangasamy College of Technology, Tiruchengode 637215, Namakkal (Dt.), Tamil Nadu, India.

⁴Centre for Research and Development, K.S.Rangasamy College of Technology, Tiruchengode 637215, Namakkal (Dt.), Tamil Nadu, India.

چکیده

This study investigates the fractional modeling of a double-intermediate enzymatic reaction model using the Caputo derivative. A system of nonlinear fractional differential equations is formulated in a dimensionless form to capture the complex dynamics of intermediate enzymes. The properties of the model are explored using key theorems related to fractional calculus. The generalized Euler method was employed to obtain numerical solutions for various fractional orders, highlighting the memory-dependent behavior of the system. The numerical simulations were consistent with the theoretical expectations, confirming the validity and effectiveness of the proposed method. Various dimensionless parameters were systematically altered, and the corresponding system responses were captured using 2D plots and surface visualizations in MATLAB\textsuperscript{\textregistered}. The simulation results highlighted that variations in these parameters significantly influenced the transient and steady-state dynamics, illustrating their biochemical relevance and the utility of the fractional-order model in capturing such sensitivities.

کلیدواژه‌ها

Enzyme reaction model؛ Dimensionless formation؛ Fractional derivative؛ Extended Euler method؛ Numerical simulation