Laplace Adomian Decomposition Method (LADM) on Approximate Solution to Fractional Order Kidnapping Dynamics
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546-562
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10.58578/mjms.v4i3.10202
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Authors:Laminu Idris1, Ahmad Rufai Tasiu2*
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Abstract
Fractional-order modeling offers a flexible framework for representing complex kidnapping dynamics through systems of nonlinear differential equations. This study developed a fractional-order compartmental model based on the Caputo derivative and applied the Laplace–Adomian Decomposition Method (LADM) to derive approximate solutions to the resulting nonlinear system. The LADM procedure generated an infinite-series representation that converged to the exact solution of the system. Numerical simulations were subsequently performed using Maple to validate the approximate solutions across fractional-order values ranging from 0.95 to 1.00. A comparison between the fractional-order and classical models showed that the fractional formulation provides greater flexibility in representing system behavior, allowing outcomes in the different compartments to be adjusted by varying the fractional order. The study demonstrates that LADM provides a convergent and computationally effective approach for solving the proposed fractional-order kidnapping model. These findings contribute to the mathematical modeling of kidnapping dynamics by providing an adaptable analytical framework for examining variations in compartmental outcomes that may not be captured as flexibly by the corresponding classical model.
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