It is eminent that partial differential equations are extensively meaningful in physics,mathematics and engineering.Natural phenomena are formulated with partial differential equations and are solved analytically or n...It is eminent that partial differential equations are extensively meaningful in physics,mathematics and engineering.Natural phenomena are formulated with partial differential equations and are solved analytically or numerically to interrogate the system’s dynamical behavior.In the present research,mathematical modeling is extended and the modeling solutions Helmholtz equations are discussed in the fractional view of derivatives.First,the Helmholtz equations are presented in Caputo’s fractional derivative.Then Natural transformation,along with the decomposition method,is used to attain the series form solutions of the suggested problems.For justification of the proposed technique,it is applied to several numerical examples.The graphical representation of the solutions shows that the suggested technique is an accurate and effective technique with a high convergence rate than other methods.The less calculation and higher rate of convergence have confirmed the present technique’s reliability and applicability to solve partial differential equations and their systems in a fractional framework.展开更多
基金Center of Excellence in Theoretical and Computational Science(TaCS-CoE)&Department of Mathematics,Faculty of Science,King Mongkut’s University of Technology Thonburi(KMUTT),126 Pracha Uthit Rd.,Bang Mod,Thung Khru,Bangkok 10140,Thailand.
文摘It is eminent that partial differential equations are extensively meaningful in physics,mathematics and engineering.Natural phenomena are formulated with partial differential equations and are solved analytically or numerically to interrogate the system’s dynamical behavior.In the present research,mathematical modeling is extended and the modeling solutions Helmholtz equations are discussed in the fractional view of derivatives.First,the Helmholtz equations are presented in Caputo’s fractional derivative.Then Natural transformation,along with the decomposition method,is used to attain the series form solutions of the suggested problems.For justification of the proposed technique,it is applied to several numerical examples.The graphical representation of the solutions shows that the suggested technique is an accurate and effective technique with a high convergence rate than other methods.The less calculation and higher rate of convergence have confirmed the present technique’s reliability and applicability to solve partial differential equations and their systems in a fractional framework.
