TY  - EJOU
AU  - Jan, Rashid 
AU  - Khan, Hassan 
AU  - Kumam, Poom 
AU  - Tchier, Fairouz 
AU  - Shah, Rasool 
AU  - Jebreen, Haifa Bin 

TI  - The Investigation of the Fractional-View Dynamics of Helmholtz Equations Within Caputo Operator
T2  - Computers, Materials \& Continua

PY  - 2021
VL  - 68
IS  - 3
SN  - 1546-2226

AB  - 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.
KW  - Fractional-order Helmholtz equations; fractional calculus; {natural} transform decomposition method; analytic solution

DO  - 10.32604/cmc.2021.015252