Application of Analytical Techniques for Solving Fractional Physical Models Arising in Applied Sciences

Abstract

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.

Modeling and Predicting Passenger Load Factor in Air Transportation: A Deep Assessment Methodology with Fractional Calculus Approach Utilizing Reservation Data

“…There are two new techniques offered: the homotopy perturbation transform and the Elzaki transform decomposition. To handle nonlinear terms efficiently, fractional derivatives in the Caputo sense are combined with Adomian and He's polynomials [26]. In a further study, modeling based on fractional-order derivatives is utilized to predict future trends in confirmed cases and deaths from the COVID-19 outbreak in India through October 2020.…”

Solvability and Mittag–Leffler–Ulam stability for fractional Duffing problem with three sequential fractional derivatives

“…In differential equations, the fractional derivative operators have shown its wings in the modeling of several problems in science, engineering, and technology as can be seen in earlier studies [1–9] and the references therein. In quite recent times, many researchers have given the existence, uniqueness, and various structures of Ulam stability and Mittag–Leffler–Ulam stability of solutions for differential equations of fractional order as in previous research [10–23] and the references therein.…”

Lattice Boltzmann Model for a Class of Time Fractional Partial Differential Equation

“…Fractional partial differential equations (FPDEs) have received an increasing attention in recent years and have been widely applied in fields such as viscoelastic materials, chemistry, engineering, biology, physics, economics, and so on [1][2][3][4][5][6][7][8][9]. Compared with the classical integer order model, the main advantage of the fractional order model lies in its capacity to effectively describe materials and processes with genetic and memory properties.…”