This study explores the dynamics of a [Formula: see text]-dimensional extended Kairat-X equation, revealing its connections to differential geometry curves and equivalence principles. Using Hirota bilinear method linear superposition principle (LSP), we derived lump-periodic solutions, higher-order solitons with bifurcations, resonant multi-soliton waves, positive complexiton solutions. To highlight significance these results, present 3D, density contour plots for specific parameter values....

<abstract><p>Mathematical formulations are crucial in understanding the dynamics of disease spread within a community. The objective this research is to investigate SEIR model SARS-COVID-19 (C-19) with inclusion vaccinated effects for low immune individuals. A mathematical developed by incorporating vaccination individuals based on proposed hypothesis. fractal-fractional operator (FFO) then used convert into fractional order. newly SEVIR system examined both qualitative and...

Abstract Nonlinear partial evolution equations are mostly significant to illustrate critical phenomena in wave theory concerning real-world problems. The current study deals with the (2 + 1)-dimensional nonlinear Fokas model depicting pulse through mono-mode optical fibers. Improved auxiliary equation and improved tanh schemes executed on considering governing system. Subsequently, a variety of soliton solutions nature dynamic waves made accessible throughout present exploration. Some...

One of the most important problems in study geometric function theory is knowing how to obtain sharp bounds coefficients that appear Taylor–Maclaurin series univalent functions. In present investigation, our aim calculate some estimates involving for family convex functions with respect symmetric points and associated a hyperbolic tangent function. These include first four initial coefficients, Fekete–Szegö Zalcman inequalities, second-order Hankel determinant. Additionally, inverse...

Abstract In this study, we acquired some optical solitons of (3 + 1) dimensional nonlinear Schrödinger equation (3DNLSE) and coupled Helmholtz equations (CNLHE) by using generalized $$\left(\frac{{G}^{\prime}}{G}\right)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mfrac> <mml:msup> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> <mml:mo>′</mml:mo> </mml:msup> </mml:mfrac> </mml:mfenced> </mml:math> -expansion method (GEM). We are able to derive exponential,...

Abstract The nonlinear Schrodinger equation is a key tool for modeling wave propagation in and dispersive&amp;#xD;media. This study focuses on the complex cubic with δ-potential,&amp;#xD;explored through Brownian process. investigation begins derivation of stochastic solitary&amp;#xD;wave solutions using modified exp(−Ψ(ξ)) expansion method. To illustrate noise effects, 3D 2D&amp;#xD;visualizations are displayed different non-negative values parameter under suitable parameter&amp;#xD;values....

Abstract Diverse aspects of real-world problems are portrayed through nonlinear Schrodinger equations. This exploration considers a pair fractional order equations describing important instability phenomena which related to heat pulse, quantum condensates, acoustics, hydrodynamics, and optics. The improved auxiliary equation tanh schemes imposed on the governing model generate bulk innovative accurate wave solutions. Plenty solutions achieved in this study could be utilized characterize...

In this article, first we deliberate the theory of Gaussian field and extension field. However, in second phase, provide a comprehensive construction scheme for BCH codes over The decoding newly designed is handled through slightly amended modified Berlekamp-Massey algorithm. coding gain obtained by Accordingly, better code rate number words are as compared to finite fields. Thus, makes them promising candidate use communication systems.

&lt;abstract&gt; &lt;p&gt;In the field of cryptography, block ciphers are widely used to provide confidentiality and integrity data. One key components a cipher is its nonlinear substitution function. In this paper, we propose new design methodology for function cipher, based on use Quaternion integers (QI). Quaternions an extension complex numbers that allow more arithmetic operations, which can enhance security cipher. We demonstrate effectiveness our proposed by implementing it in...

In this study, a novel integral operator that extends the functionality of some existing operators is presented. Specifically, acts as inverse to widely recognized Opoola differential operator. By making use operator, certain subclass analytic univalent functions defined in unit disk proposed and investigated. This new class encompasses familiar subclasses, like starlike convex functions, while ones are introduced. The investigation thereafter covers coefficient inequality, distortion,...

This study explores the thermodynamic behavior of a reactive hydromagnetic liquid flowing through permeable materials, with convective cooling applied to walls. holds practical significance in optimization thermal management systems and it is crucial for enhancing efficiency controlling runaway. The flow modeled as system partial differential equations which are numerically solved. modified Adomian Decomposition Method Pade approximation technique utilized solving equations. results acquired...

This research article introduces the four-dimensional natural transform Adomian decomposition method (FNADM) for solving (3+1)-dimensional time-singular fractional coupled Burgers’ equation, along with its associated initial conditions. The FNADM approach represents a fusion of techniques and methodologies. In order to observe influence time-Caputo derivatives on outcomes aforementioned models, two examples are illustrated their three-dimensional figures. effectiveness reliability this...

This paper is based on finding soliton solutions to fractional Kaup-Boussinesq (FKB) system. The derivatives such as β-derivative and truncated M-fractional derivative are used in this study. unified approach, generalized projective riccati equations method (GPREM) improved tan (φ(ζ)/2)-expansion approaches efficiently for obtaining bright soliton, dark singular periodic dark-singular combo dark-bright soliton. numerical simulations also carried out by 3D 2D, graphs of some the obtained...

Heat and mass transfer acquired the attention of investigators experts because massive uses in field medicine, manufacturing modern aircrafts, advanced water filtration plants, distillation process water, more efficient electronic instruments, batteries, textile industry, as manufacturer cosmetics industry defense equipment. By viewing this, we considered numerical study Fourier flux buoyancy driven forces on flow thermal diffusion transmission body revolutions (Paraboloid cone), situated a...

&lt;abstract&gt; &lt;p&gt;Multi-objective transportation problems (MOTPs) are mathematical optimization that involve simultaneously considering multiple, often conflicting objectives in planning. Unlike traditional problems, which typically focus on minimizing a single objective such as cost or distance, MOTPs aim to balance multiple find the optimal solution. These appear various real-world applications logistics, supply chain management, and transportation, where decision-makers need...

Healthcare requires efficient delivery of supplies, but things often change unexpectedly. In the field healthcare logistics, transportation efficiency plays a fateful role in ensuring timely medical equipment, and personnel. However, dynamic nature environment brings complexities, such as unexpected changes demand, disruptions, differing priorities. This research highlights novel approach to address these challenges through an innovative model designed for uncertain multi-objective...

This study discusses the connection between Fermat perfect natural vectors and some specific polynomials, whose maximal root is a number forming part of vector radius. Apart from nature construction Fermat’s examples application are given. If found as numbers, calculating roots polynomials constitutes an alternative algorithm to find out vectors.

The relevance of time-dependent magneto-free convection and its consequences for mass energy transport are being increasingly understood in science. Unfortunately, very little is known about how the fractional generalized technique would affect a complete analysis Maxwell fluid dynamics over porous plate. Using Caputo–Fabrizio time-fractional integral, Fourier thermal flux law fractionally Fick’s equation flow both generalized. appropriate similarity transformations allows us to characterize...

This article employs the q-homotopy analysis transformation method (q-HATM) to numerically solve, subject an integral condition, a fractional IBVP. The resulting numerical scheme is applied in which exact solution obtained, several test examples order illustrate its efficiency.

The triple Sumudu transform decomposition method (TSTDM) is a combination of the Adomian (ADM) and transform. It computational that can be appropriate for solving linear nonlinear partial differential equations. existence analysis derivatives theorems are proven. Finally, we solve 1+1 2+1-dimensional Boussinesq equations by applying (TSTDM)technique, which gives approximate solution with quick convergence. more precise than using ADM alone. In addition, three examples offered to examine...