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A New Scheme of the ARA Transform for Solving Fractional-Order Waves-Like Equations Involving Variable Coefficients

工程与科学中的计算机建模(英文) 2024年第1期138卷 761-791页

作者： Yu-Ming Chu Sobia Sultana Shazia Karim Saima Rashid Mohammed Shaaf Alharthi Department of Mathematics Huzhou UniversityHuzhou313000China Department of Mathematics Imam Mohammad Ibn Saud Islamic UniversityRiyadh11461Saudi Arabia Department of Basic Sciences and Humanities UET LahoreFaisalabad Campus54800Pakistan Department of Mathematics Government College UniversityFaisalabad38000Pakistan Department of Mathematics and Statistics College of ScienceTaif UniversityP.O.Box 11099Taif21944Saudi Arabia

The goal of this research is to develop a new,simplified analytical method known as the ARA-residue power series method for obtaining exact-approximate solutions employing Caputo type fractional partial differential equations(PDEs)with variable ***-transform is a robust and highly flexible generalization that unifies several existing *** key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor’s *** process of finding approximations for dynamical fractional-order PDEs is challenging,but the ARA-residual power series technique magnifies this challenge by articulating the solution in a series pattern and then determining the series coefficients by employing the residual component and the limit at infinity *** approach is effective and useful for solving a massive class of fractional-order *** appealing implementations are taken into consideration to demonstrate the effectiveness of the projected technique in creating solitary series findings for the governing equations with variable ***,several visualizations are drawn for different fractional-order *** that,the estimated findings by the proposed technique are in close agreement with the exact ***,statistical analyses further validate the efficacy,dependability and steady interconnectivity of the suggested ARA-residue power series approach.

关键词： ARA-transform Caputo fractional derivative residue-power seriesmethod analytical solutions statistical analysis

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