Effect of Space Fractional Parameter on Nonlinear Ion Acoustic Shock Wave Excitation in an Unmagnetized Relativistic Plasma

Abstract

In this work, the model equation with space fractional-order (FO) is used to investigate the nonlinear ion acoustic shock wave excitations (NIASWEs) in an unmagnetized collisionless weakly relativistic plasma having inertial relativistic ions fluid with viscous effects, inertial-less non-thermal electrons and inertial-less Boltzmann positrons. To do it, the Korteweg-de Vries Burgers equation (KdVBE) is derived from the considered fluid model equations by implementing the standard reductive perturbation method. Accordingly, such equation is converted to space fractional KdVBE via Agrawal’s variational principle with the help of the beta fractional derivative and its properties. The exact analytical solutions of KdVBE with space FO are determined via the modified Kudryashov method. The influence of space fractional and other related plasma parameters on NIASWEs are investigated. The outcomes would be useful to understand the nature of shocks with the presence of non-local or local space in many astrophysical and space environments (especially in the relativistic wind of pulsar magnetosphere, polar regions of neutron stars, etc.) and further laboratory verification.

Study of Fuzzy Fractional Third-Order Dispersive KdV Equation in a Plasma under Atangana-Baleanu Derivative

“…All the abovementioned equations succeeded in giving a good description to many nonlinear phenomena that arise and propagate within different plasma systems and many other branches of science. On the other hand, many researchers tended to model most of the mysterious phenomena in plasma physics by describing them using fractional differential equations such as fractional KdV-type equations and many related equations in higher order because they give a more accurate and comprehensive description better than the integer differential equations [59][60][61]. As a result, numerous scholars investigated the solution of many fuzzy FDEs using these models of plasma physics.…”

The Efficient Techniques for Non-Linear Fractional View Analysis of the KdV Equation

“…In this context, Hassan et al have presented the solutions of some non-linear FPDEs and their systems in [32][33][34][35]. Many Other important and efficient techniques that have been implemented to solve FPDEs and their systems are Iterative Laplace transform method [38], optimal homotopy asymptotic method (OHAM) [39], extended direct algebraic method (EDAM) [49], Adomian decomposition method (ADM) [40,41], Natural transform method [42], the Finite difference method (FDM) [43], the (G/ Ǵ)-expansion method [48], the Homotopy perturbation transform technique along with transformation (HPTM) [44,45,47], standard reductive perturbation method [50], the Haar wavelet method (HWM) [51,52], spectral collocation method (SCM) [46], the Variational iteration procedure with transformation (VITM) [58] and the differential transform method (DTM) [53][54][55]. In similar way, the novel techniques have been used for the solutions of Korteweg-de Vries equation and time-fractional Drinfeld-Sokolov-Wilson system and can be cited in [56,57].…”

Numerical and Analytical Simulations of Nonlinear Time Fractional Advection and Burger’s Equations

“…To obtain the approximate solutions to the above models, researchers use and develop a variety of analytical approaches. The frequently used methods are optimal homotopy asymptotic method (OHAM) [23], Iterative Laplace transform method [24], extended direct algebraic method (EDAM) [25], Adomian decomposition method (ADM) [26], the Finite difference method (FDM) [27], the homotopy perturbation transform technique along with transformation (HPTM) [28], the (G/G′)-expansion method [29], the Haar wavelet method (HWM) [30], standard reductive perturbation method [31], the variational iteration procedure with transformation (VITM) [32], and the differential transform method (DTM) [33]. In this context, Hassan et al have presented the solutions of some nonlinear FPDEs which can be seen in [34][35][36].…”