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 e...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 coefficient.ARA-transform is a robust and highly flexible generalization that unifies several existing transforms.The key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor’s expansion.The 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 concepts.This approach is effective and useful for solving a massive class of fractional-order PDEs.Five 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 coefficients.Additionally,several visualizations are drawn for different fractional-order values.Besides that,the estimated findings by the proposed technique are in close agreement with the exact outcomes.Finally,statistical analyses further validate the efficacy,dependability and steady interconnectivity of the suggested ARA-residue power series approach.展开更多
文摘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 coefficient.ARA-transform is a robust and highly flexible generalization that unifies several existing transforms.The key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor’s expansion.The 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 concepts.This approach is effective and useful for solving a massive class of fractional-order PDEs.Five 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 coefficients.Additionally,several visualizations are drawn for different fractional-order values.Besides that,the estimated findings by the proposed technique are in close agreement with the exact outcomes.Finally,statistical analyses further validate the efficacy,dependability and steady interconnectivity of the suggested ARA-residue power series approach.
