TY - JOUR
T1 - Application of Analytical Techniques for Solving Fractional Physical Models Arising in Applied Sciences
AU - AlBaidani, Mashael M.
AU - Ganie, Abdul Hamid
AU - Aljuaydi, Fahad
AU - Khan, Adnan
N1 - Publisher Copyright:
© 2023 by the authors.
PY - 2023/8
Y1 - 2023/8
N2 - In this paper, we examined the approximations to the time-fractional Kawahara equation and modified Kawahara equation, which model the creation of nonlinear water waves in the long wavelength area and the transmission of signals. We implemented two novel techniques, namely the homotopy perturbation transform method and the Elzaki transform decomposition method. The derivative having fractional-order is taken in Caputo sense. The Adomian and He’s polynomials make it simple to handle the nonlinear terms. To illustrate the adaptability and effectiveness of derivatives with fractional order to represent the water waves in long wavelength regions, numerical data have been given graphically. A key component of the Kawahara equation is the symmetry pattern, and the symmetrical nature of the solution may be observed in the graphs. The importance of our suggested methods is illustrated by the convergence of analytical solutions to the precise solutions. The techniques currently in use are straightforward and effective for solving fractional-order issues. The offered methods reduced computational time is their main advantage. It will be possible to solve fractional partial differential equations using the study’s findings as a tool.
AB - In this paper, we examined the approximations to the time-fractional Kawahara equation and modified Kawahara equation, which model the creation of nonlinear water waves in the long wavelength area and the transmission of signals. We implemented two novel techniques, namely the homotopy perturbation transform method and the Elzaki transform decomposition method. The derivative having fractional-order is taken in Caputo sense. The Adomian and He’s polynomials make it simple to handle the nonlinear terms. To illustrate the adaptability and effectiveness of derivatives with fractional order to represent the water waves in long wavelength regions, numerical data have been given graphically. A key component of the Kawahara equation is the symmetry pattern, and the symmetrical nature of the solution may be observed in the graphs. The importance of our suggested methods is illustrated by the convergence of analytical solutions to the precise solutions. The techniques currently in use are straightforward and effective for solving fractional-order issues. The offered methods reduced computational time is their main advantage. It will be possible to solve fractional partial differential equations using the study’s findings as a tool.
KW - Adomian decomposition method
KW - Caputo operator
KW - Elzaki transform
KW - Kawahara and modified Kawahara equations
KW - homotopy perturbation method
UR - http://www.scopus.com/inward/record.url?scp=85169003189&partnerID=8YFLogxK
U2 - 10.3390/fractalfract7080584
DO - 10.3390/fractalfract7080584
M3 - Article
AN - SCOPUS:85169003189
SN - 2504-3110
VL - 7
JO - Fractal and Fractional
JF - Fractal and Fractional
IS - 8
M1 - 584
ER -