A new analysis for fractional model of regularized long‐wave equation arising in ion acoustic plasma waves

Abstract

Communicated by C. CuevasThe key purpose of the present work is to constitute a numerical scheme based on q-homotopy analysis transform method to examine the fractional model of regularized long-wave equation. The regularized long-wave equation explains the shallow water waves and ion acoustic waves in plasma. The proposed technique is a mixture of q-homotopy analysis method, Laplace transform, and homotopy polynomials. The convergence analysis of the suggested scheme is verified. The scheme provides¯and n-curves, which show that the range convergence of series solution is not a local point effects and elucidate that it is superior to homotopy analysis method and other analytical approaches.

A fractional-order form of a system with stable equilibria and its synchronization

“…The identification of hidden attractors in practical applications is important to avoid the sudden change to undesired behavior [29]. Previous research has established that derivatives are important in the field of mathematical modeling [51][52][53][54]. Fractional-order system (5) involving derivative orders is a generalization of autonomous system (1).…”

“…Different definitions and main properties of fractional calculus have been reported in the literature [47][48][49][50]. The fractional derivatives play important roles in the field of mathematical modeling of numerous models such as fractional model of regularized long-wave equation [51], Lienard's equation [52], fractional model of convective radial fins [53], modified Kawahara equation [54], etc. In recent years, there has been an increasing interest in the stability of fractional systems [55][56][57].…”

Combined ZK-mZK equation for Rossby solitary waves with complete Coriolis force and its conservation laws as well as exact solutions

“…Numerous powerful methods have been used to seek the conservation laws: Laplace direct technique [34], characteristic form given by Stuedel [35], q-homotopy analysis transform method (q-HATM) [36], multiplier approach [37,38]. In this thesis, based on the modified CamassaHolm equation [39] and ZK-BBM equations [40] for each multiplier, and the method of Ibragimov (nonlocal conservation method) [41][42][43], using the multiplier approach, conservation laws and the corresponding conserved quantities are discussed.…”

On the generalized solutions of a certain fourth order Euler equations

“…For numerical solution, Singh et al [21] studied the numerical solution of the damped Berger's equation by using the concept of an iterative method. Moreover, there are works on analytical and numerical techniques to solve differential equations, see [14,15,22,24] for more details.…”