The thermal case study is conducted by using artificial intelligence to examine the heat transfer traits in Williamson fluid flow with source and slip effects. field interacts externally applied magnetic velocity additionally considered at surface. formulated terms of energy momentum equations. All inputs (Prandtl number, field, slip, Weissenberg number) are represented a 4 × 72 matrix samples Nusselt number 1 matrix. randomly divided into three stages: 70%(50) for training, 15%(11) each...

<abstract><p>This paper presents a significant contribution in the form of new general equation, namely $ \mathfrak{q} $-deformed equation or tanh-Gordon equation. The introduction this novel opens up possibilities for modeling physical systems that exhibit violated symmetries. By employing (G'/G) expansion method, we have successfully derived solitary wave solutions newly defined under specific parameter regimes. These provide valuable insights into behavior system and its...

By following the statistics, over last few years, use of Artificial Intelligence conjectured with mathematical models has increased abundantly for physical problems having thermal engineering standpoints. Owning to such importance, we offer Levenberg-Marquadt-based neural networking modeling non-Newtonian fluid flow at a flat heat-generating surface and velocity slip effects. A tangent hyperbolic (THF) is considered transfer heat mass. Heat absorption generation aspects are carried out by...

Several types of solitary wave solutions (3 + 1)-dimensional nonlinear extended and modified quantum Zakharov–Kuznetsov equations are established successfully via the implantation three mathematical methods. The concerned models have many fruitful applications to describe waves in electron–positron–ion magnetoplasmas weakly ion-acoustic plasma. derived results MEAEM method, ESE F-expansion been retrieved will be expedient future illuminate collaboration between lower waves. For physical...

A telegraph equation is believed to be an appropriate model of population dynamics as it accounts for the directional persistence individual animal movement. Being motivated by problem habitat fragmentation, which known a major threat biodiversity that causes species extinction worldwide, we consider reaction–telegraph (i.e., combined with growth) on bounded domain goal establish conditions survival. We first show analytically that, in case linear growth, expression domain’s critical size...

This study aims to explore the ways in which population dynamics are affected by shape and size of fragmented habitats. Habitat fragmentation has become a key concern ecology over past 20 years as it is thought increase threat extinction for number plant animal species; particularly those close fragment edge. In this study, we consider issue using mathematical modelling computer simulations several domains various with different strength Allee effect. A two-dimensional reaction-diffusion...

Very recently, the system of differential equations governing three-dimensional falling body problem (TDFBP) has been approximately solved. The previously obtained approximate solution was based on fact that Earth’s rotation (ER) is quite slow and hence all high order terms ω in addition to magnitude ω2R were neglected, where angular velocity R radius Earth. However, it shown this paper ignorance such magnitudes leads, many cases, significant errors estimated time other physical quantities....

<abstract><p>The COVID-19 pandemic still gains the attention of many researchers worldwide. Over past few months, China faced a new wave this which increases risk its spread to rest world. Therefore, there has become an urgent demand know expected behavior in coming period. In regard, are mathematical models from we may obtain accurate predictions about pandemic. Such target be achieved via updating taking into account memory effect fractional calculus. This paper generalizes...

Splenic cysts in the pediatric population are rare but can present with a range of clinical manifestations. Acute abdominal pain, although uncommon, is significant presentation that requires prompt evaluation and management. We case an 11-year-old female who presented to emergency department severe left upper quadrant pain 24 hours’ duration. Physical examination revealed tenderness guarding palpable, firm mass. Elevated serum amylase lipase levels initially raised suspicion pancreatic...

Understanding of the dynamics riots, protests, and social unrest more generally is important in order to ensure a stable, sustainable development various groups, as well society whole. Mathematical models have been increasingly recognized powerful research tool facilitate progress this field. However, question what should be an adequate mathematical framework describe corresponding processes largely open. In particular, great majority previous studies dealt with non-spatial or spatially...

In the current assessment, computational analysis is performed to study heat and mass transfer characteristics over an inclined surface embedded in porous materials. electromagnetic fields (EMF) environment, impact of buoyancy forces (arise from both temperature concentration) thoroughly investigated chemically reactive flow. A revamped Scott–Blair model introduced constitutive equations control flow velocity at highly charged surface. order perform simulations, stabilized finite element...

<p>This paper presented the formulation and solution of time fractional q-deformed tanh-Gordon equation, a new extension to traditional equation using calculus, q-deformation parameter. This aimed better model physical systems with violated symmetries. The approach taken involved controlled Picard method combined Laplace transform technique Caputo derivative find solutions this equation. Our results indicated that was effective highlighted our in addressing We explored both existence...

Summary This paper contributes to the study of a new model called ‐deformed equation or tanh‐Gordon model. To understand physical systems with violated symmetries. We utilize ‐expansion approach solve for specific parameter values. method generates solutions that provide valuable insights into system's dynamics and behavior. verify accuracy our solutions, we also apply finite difference technique obtain numerical equation. dual ensures reliability results. present findings using tables...

Abstract In this study, we introduce an efficient analysis of a new equation, termed the time-fractional <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>q</m:mi> </m:math> q -deformed tanh-Gordon equation (TGE), which is fractional form TGE that was recently introduced by Ali and Alharbi. This represents significant advancement in field mathematical physics, due to its applications many fields including superconductivity fiber optics. It has condensed matter physics modeling...

This paper analyzes the first-order delay equation y′(t)=αy(t)+βy(t−τ) subject to a history function in addition an initial condition that assumes discontinuity at t=0. The method of steps is successfully applied derive exact solution explicit form. In addition, unified formula provided describe any finite sub-interval problem’s domain. characteristics and properties are theoretically investigated then confirmed through several plots. behavior its derivative examined interpreted. results...

When population units fail for several reasons, the competing risks model is triggered. The failure time and associated reason of are noted in this model. It possible to partially observe reasons why fails. In work, where distributed with power hazard rate distribution, we utilize under observed failure. We develop maximum likelihood estimators parameters related estimated confidence intervals based on independent type-I censoring data. Two distinct approaches used construct bootstrap point...

The fractional generalization of the Ambartsumian delay equation with Caputo’s derivative is considered. very difficult to be solved neither in case ordinary derivatives nor derivatives. In this paper we combine Laplace transform Adomian decomposition method solve studied equation. exact solution obtained as a series which terms are expressed by Mittag-Leffler functions. advantage present approach over known literature ones discussed.