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All Journal Al-Jabar : Jurnal Pendidikan Matematika Desimal: Jurnal Matematika
Rahman, Hiwa Hussein
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Education Mathematics Social Sciences

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Leveraging the Anuj transform: A novel approach to modeling population dynamics in interdisciplinary sciences Hilmi, Hozan; Jalil, Shabaz; Rahman, Hiwa Hussein; Faraj, Bawar Mohammed
Al-Jabar: Jurnal Pendidikan Matematika Vol 15 No 2 (2024): Al-Jabar: Jurnal Pendidikan Matematika
Publisher : Universitas Islam Raden Intan Lampung, INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ajpm.v15i2.23494

Abstract

This study introduces the Anuj transform as an innovative tool for addressing population growth and decay problems. By applying the Anuj transform, we demonstrate its efficacy and practical value in solving these complex issues. The paper presents several applications that highlight the transformative potential of the Anuj transform in modeling population dynamics. The results underscore the utility of this method, providing clear solutions without extensive calculations.
Memory effects and sustainable harvesting in a fractional-order predator-prey model with prey refuge and nonlinear harvesting Rahman, Hiwa Hussein; Faraj, Bawar Mohammed
Desimal: Jurnal Matematika Vol. 8 No. 2 (2025): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/94h4r762

Abstract

This study investigates the dynamics of a predator-prey model with fractional-order derivatives, incorporating factors such as prey refuge, nonlinear harvesting, and memory-dependent processes. The model is governed by a coupled system of Caputo fractional differential equations, where prey growth follows logistic dynamics with refuge parameter , and harvesting adopts a generalized nonlinear form. The predator’s functional response follows a Holling type II mechanism modified by prey refuge. We analyze existence, uniqueness, and stability of equilibrium points, along with the influence of fractional-order derivative  on long-term behavior. Numerical simulations reveal that memory effects significantly alter system dynamics, leading to sustained oscillations, enhanced stability, or complex bifurcation patterns compared to classical integer-order models. Furthermore, we explore sustainable harvesting strategies by examining the impact of refuge and harvesting efforts on population persistence. Our findings highlight ecological implications of fractional-order dynamics in predator-prey systems, providing insights into biodiversity conservation and resource management.
Co-Authors Faraj, Bawar Mohammed Hilmi, Hozan Jalil, Shabaz