Search

This research article aims to get superabundant wave solutions of the fractional nonlinear space–time telegraph via two computational schemes (modified Khater (MK) method and simplest equation (SE) method) through a new fractional operator (Atangana–Baleanu [AB] fractional derivative). These solutions are used to calculate the boundary and initial conditions that allow applying the B‐spline collection schemes for constructing the numerical solutions and absolute value of error between obtained exact and numerical solutions. On the other hand, the second goal of this research is to investigate the accuracy of used computational schemes and their constructed solutions, where the investigated model is one of the most attractive models for studying in the electrified transmission or electromagnetic waves. This model, which is used to illustrate as the electromagnetic waves do keep mirrored about the wire, or that suspense patterns perform exhibit along the line, describes the cutting‐edge or voltage of an electrified transmission range with the day yet distance. Oliver Heaviside formulated this model in 1880. [ABSTRACT FROM AUTHOR]

In this paper, the generalized exponential (GExp) method has been employed to construct novel solitary wave solutions of the nonlinear fractional biological population (FBP) model. This model is used to demonstrate the relation of the population with deaths and births. Many novel traveling wave solutions have been formulated in distinct forms such as exponential, hyperbolic and trigonometric forms. These solutions have been explained in three different axes. The first axis is plotting them in their three optional (real, imaginary and absolute value), the second axis is handling these solutions for constructing the requested conditions for applying trigonometric quintic B-spline (TQBS) scheme. The second one determines the accuracy of the obtained analytical solutions by showing the error's value between the analytical and numerical solutions. At the same time, the third one is comparing our analytical and numerical solutions, which have recently been published that explain the paper's contribution and novelty. [ABSTRACT FROM AUTHOR]

In this paper, the solitary wave solutions of the complex perturbed Gerdjikov–Ivanov (CPGI) equation are investigated by employing the extended simplest equation (ESE) and modified Khater (MKhat) methods. The studied equation describes the physical characterization of the optical soliton waves to mitigate internet bottlenecks with many different applications in the telecommunication industry. The evaluated solutions are explained through various sketches in two-, three-dimensional, and contour plots of their real, imaginary, and absolute values. The novelty of the obtained results is demonstrated by comparing them with the previously obtained solutions. The computational applied schemes' performance is tested to illustrate their powerful and effective handling of many nonlinear evolutions equations. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear fractional Lotka–Volterra model is analyzed and numerically studied. This research is based on applying the three latest analytical schemes and three other numerical schemes to construct rich wave solutions. In different forms, many novel solitary wave solutions are built and presented in two-dimensional, three-dimensional, and contour plots. The numerical method conditions are evaluated through the obtained analytical solutions, and the accuracy of the analytical solutions is studied. Many numerical solutions are constructed based on the employed schemes. Additionally, the analytical, semi-analytical, numerical, and absolute values of error between the values of obtained solutions are calculated with the different values of the given variable in the solutions. Furthermore, the match between the obtained analytical solution and the numerical solution has been explained through some two-dimensional distributed radar charts. The contribution of this article is demonstrated by comparing the obtained solution with the recently published results of the same model. [ABSTRACT FROM AUTHOR]

This manuscript employs the trigonometric Quintic B‐spline (TQBS) scheme for investigating the numerical solution of the conformable fractional nonlinear time‐space telegraph equation. This model is derived by Oliver Heaviside 1880 to describe the cutting‐edge or voltage of an electrified transmission range with the day yet distance from an electrified transmission or electromagnetic wave's application. In Hamed and Khater, three recent computational schemes (sech–tanh expansion method; extended sinh–Gorden expansion method; and extended simplest equation method) have been applied to the fractional model for constructing the exact traveling wave solutions. Many distinct solutions have been obtained, and some of them have been sketched in two, three‐dimensional, and density plots. Here, these solutions are investigated to evaluate the initial and boundary conditions that apply the suggested numerical scheme. The accuracy of the constructed exact solutions is investigated by calculating the absolute value of error. The most accurate numerical schemes of the three applied computational schemes have been illustrated. [ABSTRACT FROM AUTHOR]

This paper investigates the analytical and semi‐analytical solutions of the time‐fractional Cahn–Allen equation, which describes the structure of dynamic for phase separation in Fe‐Cr‐X (X = Mo, Cu) ternary alloys. We apply a modified auxiliary equation method and the Adomian decomposition method to get distinct solutions to our suggested model. These solutions describe the dynamic of the phase separation in iron alloys and use in solidification and nucleation problems. The applications of this method arise in many various fields such as plasma physics, quantum mechanics, mathematical biology, and fluid dynamics. We apply a conformable fractional derivative to this fractional model to convert it into a nonlinear partial differential equation with integer order. We obtain many analytical wave solutions and also apply a semi‐analytical scheme to calculate the absolute value of error. All solutions are verified by using Mathematica software. [ABSTRACT FROM AUTHOR]

This paper studies the analytical and semi-analytical wave solutions for the longitudinal wave equation. Moreover, it examines the performance of the modified auxiliary equation method and Adomian decomposition method on this model. This model describes the dispersion in the circular rod that dispersion caused by the transverse Poisson's effect in electro-magneto-elastic. Many explicit wave solutions are found by using the analytical technique. These solutions allow studying the physical properties of this model. The comparison between the analytical and semi-analytical solutions is discussed to show the value of the absolute error between them. [ABSTRACT FROM AUTHOR]

In this paper, the weakly nonlinear shallow-water wave model is mathematically investigated by applying the modified Riccati-expansion method and Adomian decomposition method. This model is used to describe the propagation of waves in weakly nonlinear and dispersive media. We obtain exact and solitary wave solutions of this model by using the modified Riccati-expansion method then using these solutions to determine the boundary and initial conditions. These conditions are employed to evaluate the semi-analytical wave solutions and calculate the absolute value of error. The values of absolute error show the accuracy of the obtained solutions. Some solutions are sketched to show the perspective view of the solution of this model. Moreover, the novelty of the obtained solutions is illustrated by showing the similarity and differences between our and previous solutions of the model. [ABSTRACT FROM AUTHOR]