The time-fractional generalized Burger–Fisher equation (TF-GBFE) has various applications across scientific and engineering disciplines. It is used for investigating phenomena, including the dynamics of fluid flow, gas dynamics, shock-wave formation, heat transfer, population diffusion transport, among other areas research. By incorporating fractional calculus into these models, researchers can more effectively represent non-local memory-dependent effects frequently observed in natural...

Damped Burger’s equation describes the characteristics of one-dimensional nonlinear shock waves in presence damping effects and is significant fluid dynamics, plasma physics, other fields. Due to potential applications this equation, thus objective investigation solve analyze time fractional form using methods with precise efficiency, high accuracy, ease application calculation, flexibility dealing more complicated equations, which are called Aboodh residual power series method transform...

This paper explores some innovative and modern techniques for analyzing the family of fractional Burgers-type equations, which are extensively utilized in studying shock waves plasma physics marine environments. The most notable novel effective technique employed this study first time is “ Tantawy Technique,” named after its creator, Prof. Samir El-Tantawy. Two other methods, known as, Aboodh residual power series method (ARPSM) new iteration (ANIM), also applied to analyze suggested...

The family of Fokker–Planck (FP) equations has been widely used in various physical applications, especially optical physics. It proven effective understanding numerous nonlinear phenomena observed fiber. Accordingly, we analyze the time fractional FP (FFP) to understand underlying mechanics described by suggested models, control generation and propagation these phenomena, or prevent their occurrence altogether achieve desired applications. Thus, this investigation, some techniques, such as...

In this work, a damped modified Kawahara equation (mKE) with cubic nonlinearity and two dispersion terms including the third- fifth-order derivatives is analyzed. We employ an effective semi-analytical method to achieve goal set for study. For purpose, ansatz implemented find some approximate solutions mKE. Based on proposed method, different formulas analytical symmetric approximations are formally obtained. The derived could be utilized studying all traveling waves described by mKE, such...

Multi-soliton interaction of nonlinear ion sound waves in a pair-ion–electron (PIE) plasma having non-Maxwellian electrons including Kappa, Cairns, and generalized two spectral index distribution functions is studied. To this end, modified Korteweg–de Vries (mKdV) equation obtained to investigate the ion-acoustic PIE at critical composition. The effects temperature density ratios electron velocity distributions on overtaking solitons are explored detail. results reveal that both hump...

In view of the recent observations by plasma science-spacecraft-voyager and Cassini spectrometer Saturn's magnetosphere, interaction between two counter-propagating ion-acoustic (IA) solitons is studied in an unmagnetized consisting warm adiabatic ions addition to hot cold electrons following kappa distribution. The head-on collision IA investigated using extended Poincare–Lighthill–Kuo technique. Since this model supports both compressive rarefactive solitons, therefore, soliton collisions...

The presence of the geometrical curvature makes planar Korteweg–de Vries (KdV) equation inadequate to describe propagation nonlinear waves. In many scientific disciplines including plasma physics, optics, oceanography, and communications, cylindrical KdV (CKdV) becomes appropriate choice for modeling these Motivated by applications, Bäcklund transformation is used analyze find an analytical solution CKdV in present investigation. For first time, multi-soliton solutions, single-, two-,...

This article discusses two simple, complication-free, and effective methods for solving fractional-order linear nonlinear partial differential equations analytically: the Aboodh residual power series method (ARPSM) transform iteration (ATIM). The Caputo operator is utilized to define fractional order derivatives. In these methods, analytical approximations are derived in form. We calculate first terms of then estimate absolute error resulting from leaving out remaining ensure accuracy...

This investigation analyzes the propagation of nonlinear ion-acoustic waves (IAWs) in an unmagnetized, collisionless plasma composed inertial positive ions and inertialess Maxwellian positrons as well non-Maxwellian electrons that obey (r, q)-distribution. To observe impact particle trapping on IAWs electron–positron–ion plasma, Korteweg–De Vries (KdV) modified KdV (mKdV) equations are derived using a reductive perturbation method. In distribution function, spectral parameters q) put up...

This article utilizes the Aboodh residual power series and transform iteration methods to address fractional nonlinear systems. Based on these techniques, a system is introduced achieve approximate solutions of Korteweg-de Vries (KdV) equations coupled Burger’s with initial conditions, which are developed by replacing some integer-order time derivatives derivatives. The described in Caputo sense. As result, for partial differential may be easily used generate explicit numerical equations....

<abstract> <p>The neutron diffusion equation (NDE) is one of the most important partial differential equations (PDEs), to describe behavior in nuclear reactors and many physical phenomena. In this paper, we reformulate problem via Caputo fractional derivative with integer-order initial conditions, whose meanings, case, are very evident by describing whole-time domain processing. The main aim work present analytical exact solutions (F-NDE) delayed neutrons group using Laplace...

The effects of trapping relativistically degenerate electrons are studied on the formation and interaction nonlinear ion-acoustic solitary waves (IASWs) in quantum plasmas. These plasmas detected high-density astrophysical entities can be created laboratory by interacting powerful lasers with matter. formula for number density a state relativistic degeneracy is provided, along an analysis non-relativistic ultra-relativistic scenarios. While previous studies have delved into specific aspects...

In this paper, a numerical examination of propagating nonlinear dissipative dust-acoustic breathers and rogue waves (RWs) in electron depleted dusty plasmas having two superthermal ions different temperature has been made. An important ingredient study is the inclusion effect due to viscosity dust grains evolution wave equation. Accordingly, damped/modified Schrödinger equation (DNLSE), i.e. standard (NLSE) addition damping term, obtained using reductive perturbation (the derivative...

The dynamics and collisions of dust acoustic (DA) shock excitations traveling in opposite directions are theoretically investigated a three-dimensional self-gravitating magnetized electron-depleted dusty plasma whose ingredients extremely warm positively negatively charged massive grains as well ions that follow the q-nonextensive distribution. A linear analysis extended Poincare–Lighthill–Kuo method used to derive dispersion relation, two-sided Korteweg–de Vries Burgers equations, phase...

The fractional Schrödinger–Korteweg-de Vries (S-KdV) equation is an important mathematical model that incorporates the nonlinear dynamics of KdV with quantum mechanical effects described by Schrödinger equation. Motivated several applications mentioned evolution equation, in this investigation, Laplace residual power series method (LRPSM) employed to analyze S-KdV framework Caputo operator. By incorporating both operator and derivatives into we can account for memory non-local behavior....

In this article, we present a modified strategy that combines the residual power series method with Laplace transformation and novel iterative technique for generating solution to fractional nonlinear Belousov–Zhabotinsky (BZ) system. The proposed techniques use Laurent in their development. new procedures’ advantages include accuracy speed obtaining exact/approximate solutions. suggested approach examines BZ system describes flow motion pipe.

This paper comprehensively investigates the oblique propagation of ion-acoustic solitary waves (IASWs) with arbitrary amplitude in a magnetoplasma consisting inertialess non-Maxwellian (nonthermal) electrons, Maxwellian positrons, and inertial adiabatically heated ions. It is postulated that positive ions demonstrate adiabatic behavior distinguished by anisotropic thermal pressure. The study utilizes Sagdeev's pseudopotential theory to analyze fluid equations plasma model reduce them energy...

Using the hydrodynamic equations of cold inertial positive ions with Maxwellian distribution for light negative ion and electron densities Poisson equation, family nonplanar (cylindrical spherical) Korteweg-de Vries (KdV) equations, i.e., KdV, modified extended KdV (EKdV), are obtained small but finite amplitude ion-acoustic waves. The EKdV equation is used to analyze time-dependent planar soliton shock structures. It well-known that exact solutions not possible. Therefore, a local...

This study investigates the wave solutions of time-fractional Sawada–Kotera–Ito equation (SKIE) that arise in shallow water and many other fluid mediums by utilizing some most flexible high-precision methods. The SKIE is a nonlinear integrable partial differential (PDE) with significant applications dynamics mechanics. However, traditional numerical methods used for analyzing this are often plagued difficulties handling fractional derivatives (FDs), which lead to finding techniques overcome...

This study examines the nonlinear dynamics of high-frequency electron–acoustic waves (EAWs) in a collisionless, unmagnetized plasma consisting several components, including inertial cold electrons, an electron beam, and inertialess Cairns-distributed hot electrons addition to background stationary ions. We use pseudopotential (Sagadeev potential) method investigate possibility stationary-profile solitons (EASs). In this study, nonthermal parameter, temperature ratio between density ratios,...