Solitary Wave Solutions for Some Fractional Evolution Equations via New Kudryashov Approach

In this work, we construct solitary wave solutions of a nonlinear evolution equation in the physical phenomena of waves;namely the time-fractional fifth-order Sawada-Kotera equation and the (4+1)-dimensional space-time fractional Fokas equation by Kudryashov method with a new function. As a result, new types of exact analytical solutions are obtained. Here the fractional derivative is described in beta sense.

Research on sensitivity analysis and traveling wave solutions of the (4+1)-dimensional nonlinear Fokas equation via three different techniques

In the current manuscript, (4+1) dimensional Fokas nonlinear equation is considered to obtain traveling wave solutions. Three renowned analytical techniques, namely the generalized Kudryashov method (GKM), the modified extended tanh technique, exponential rational function method (ERFM) are applied to analyze the considered model. Distinct structures of solutions are successfully obtained. The graphical representation of the acquired results is displayed to demonstrate the behavior of dynamics of nonlinear Fokas equation. Finally, the proposed equation is subjected to a sensitive analysis.

Numerical and analytical investigation for solutions of fractional Oskolkov–Benjamin–Bona–Mahony–Burgers equation describing propagation of long surface waves

In this paper, a novel meshless numerical scheme to solve the time-fractional Oskolkov–Benjamin–Bona–Mahony–Burgers-type equation has been proposed. The proposed numerical scheme is based on finite difference and Kansa-radial basis function collocation approach. First, the finite difference scheme has been employed to discretize the time-fractional derivative and subsequently, the Kansa method is utilized to discretize the spatial derivatives. The stability and convergence analysis of the time-discretized numerical scheme are also elucidated in this paper. Moreover, the Kudryashov method has been utilized to acquire the soliton solutions for comparison with the numerical results. Finally, numerical simulations are performed to confirm the applicability and accuracy of the proposed scheme.

Numerical simulations of Zakharov’s (ZK) non-dimensional equation arising in Langmuir and ion-acoustic waves

The trigonometric quintic B-spline scheme is used in this research paper to research Zakharov’s (ZK) nonlinear dimensional equation’s numerical solution. The ZK model’s solutions explain the relationship between the high-frequency Langmuir and the low-frequency ion-acoustic waves with many applications in optical fiber, coastal engineering, and fluid mechanics of electromagnetic waves, plasma physics, and signal processing. Three recent computational schemes (the expanded [Formula: see text]-expansion method, generalized Kudryashov method, and modified Khater method) have recently been used to investigate this model’s moving wave solution. Many innovative solutions have been established in this paper to determine the original and boundary conditions that allow numerous numerical schemes to be implemented. Here, the trigonometric quintic B-spline method is used to analyze the precision of the collected analytical solutions. To illustrate the precision of the numerical and computational solutions, distinct drawings are depicted.

New exact solutions for nonlinear Atangana conformable Boussinesq-like equations by new Kudryashov method

In this work, we investigate a new Kudryashov method (NKM) to find the exact and some new solutions of four different types of nonlinear Atangana conformable Boussinesq-like equations (NLACBEs). This is an appropriate algorithm for finding the exact solutions and also working for different types of nonlinear confirmable differential equations. In coastal and ocean engineering, some physical phenomenon is based on the exact solutions of the NLACBEs.

Soliton Solutions for space-time fractional Heisenberg ferromagnetic spin chain equation by generalized Kudryashov method and modified exp -expansion function method

This paper addresses the Heisenberg ferromagnetic spin chain equation with beta time derivative. Integration schemes are used to study this equation. They are generalized Kudryashov method and modified exp -expansion function method. Dark, bright and dark-bright soliton solutions of this equation are procured.