A variety of fractional soliton solutions for three important coupled models arising in mathematical physics

This paper deals with the optical solitons of fractional coupled Boussinesq, Burgers-type and mKdV equations by the hypothesis of traveling wave and [Formula: see text]-expansion scheme. These equations are important in different fields such as propagation of long water waves, fluid dynamics, and shallow water wave propagation. In comparison to other analytical procedures, the analytical methodology [Formula: see text] is an incredibly beneficial approach. This technique can also be used with other nonlinear fractional models. The suggested method generates three distinct solutions such as trigonometric, hyperbolic, and rational. Moreover, graphical representation has been used to portray the physical significance of the constructed solutions. Finally, a comprehensive study is made by using a definition of Beta fractional derivative and obtained solutions are represented graphically to understand considered models.

An Analytical Technique Implemented in the Fractional Clannish Random Walker’s Parabolic Equation with Nonlinear Physical Phenomena

In this paper, the adapted (G’/G)-expansion scheme is executed to obtain exact solutions to the fractional Clannish Random Walker’s Parabolic (FCRWP) equation. Some innovative results of the FCRWP equation are gained via the scheme. A diverse variety of exact outcomes are obtained. The proposed procedure could also be used to acquire exact solutions for other nonlinear fractional mathematical models (NLFMMs).

Flexible Transmission Network Expansion Planning Based on DQN Algorithm

Compared with static transmission network expansion planning (TNEP), multi-stage TNEP is more in line with the actual situation, but the modeling is also more complicated. This paper proposes a new multi-stage TNEP method based on the deep Q-network (DQN) algorithm, which can solve the multi-stage TNEP problem based on a static TNEP model. The main purpose of this research is to provide grid planners with a simple and effective multi-stage TNEP method, which is able to flexibly adjust the network expansion scheme without replanning. The proposed method takes into account the construction sequence of lines in the planning and completes the adaptive planning of lines by utilizing the interactive learning characteristics of the DQN algorithm. In order to speed up the learning efficiency of the algorithm and enable the agent to have a better judgment on the reward of the line-building action, the prioritized experience replay (PER) strategy is added to the DQN algorithm. In addition, the economy, reliability, and flexibility of the expansion scheme are considered in order to evaluate the scheme more comprehensively. The fault severity of equipment is considered on the basis of the Monte Carlo method to obtain a more comprehensive system state simulation. Finally, extensive studies are conducted with IEEE 24-bus reliability test system, and the computational results demonstrate the effectiveness and adaptability of the proposed flexible TNEP method.

A Novel Spectral Modified Pell Polynomials for Solving Singular Differential Equations

This paper studies the modified Pell polynomials. Some important properties of modified Pell polynomials are presented. An exact formula of modified Pell polynomials derivative in terms of modified Pell themselves is first derived with the proof and then a new relationship is constructed which relates the modified Pell polynomials expansion coefficients of a derivative in terms of their original expansion coefficients. An interesting new formula for the product operational matrix of modified Pell polynomials is also derived in this work. With modified Pell polynomials expansion scheme, the powers 1, x, …, xn are expressed in terms of such polynomials. The main goal of all presented formulas is to simplify the original equations and the determination of the coefficients of expansion based on modified Pell polynomials will be easy. Spectral techniques together with all the derived formulas of modified Pell polynomials are utilized to solve some singular initial value problems. Three test examples are solved in this work to illustrate the validity of the proposed method. The computational method is replaced by exact and explicit formulas. More accurate results are obtained than those presented by other existing methods in the literature.

Search of stable structures in cation deficient (V,Nb)CoSb half-Heusler alloys by an atomic cluster expansion

Using a cluster expansion scheme, we evaluate the structural stability of (V, Nb)CoSb half-Heusler alloys over a wide range of V and Nb concentrations when the alloy is simultaneously subject...