Modified-Laplace Transform Based Variational Iteration Method for Solving Nonlinear Fractional Order Differential Equations of Caputo-Fabrizio Type
Keywords:
Fractional Modified Laplace Transform Scheme, Variational Iteration Method, Fractional-order differential equations, Caputo-Fabrizio typeAbstract
Fractional-order differential equations have become vital tools for accurately modelling processes with memory and hereditary properties in various fields such as engineering, physics and applied mathematics. However, solving such equations—particularly those involving the Caputo-Fabrizio derivative—poses analytical and numerical challenges due to their nonlocal behaviour. This study introduces a novel hybrid computational technique: the modified Laplace transform-based variational iteration method (MLTVIM), designed specifically to tackle these challenges efficiently. The method synergistically combines the modified Laplace transform, which simplifies fractional-order equations into algebraic form, with the variational iteration method, which effectively handles the nonlinear components. A strong theoretical foundation underpins the development of the method, including convergence analysis and supporting theorems that confirm its mathematical soundness. To validate the effectiveness of MLTVIM, the approach is applied to several benchmark fractional differential equations. The results of numerical experiments demonstrate that the proposed method outperforms traditional techniques in terms of accuracy, speed of convergence, and computational efficiency. The error analysis confirms that MLTVIM achieves lower approximation errors, making it a robust and precise tool for modelling complex dynamic systems. This research contributes a reliable and powerful approach to solving complex fractional models, offering significant potential for applications in science and engineering where memory-dependent behavior is prevalent.
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