Abstract Fins are widely used in many industrial applications, including heat exchangers. They benefit from a relatively economical design cost, lightweight, and quite miniature. Thus, this study investigates the influence of wavy fin structure subjected to convective effects with internal generation. The thermal distribution, considered steady condition one dimension, is described by unique implementation physics-informed neural network (PINN) as part machine-learning intelligent strategies...

Abstract The present study scrutinizes the significance of heat source/sink (HSS), thermophoretic particle deposition, and porous media on time-dependent ternary nanofluid stream across a stretchable surface in presence Newtonian heating (NH) common wall temperature (CWT) cases. governing equations investigated model are changed into ordinary differential by using suitable similarity transformations. resultant dimensionless solved Laguerre polynomial collocation method. For comparison, Runge...

In this paper, we introduce a new type of integral transforms, called the ARA transform that is defined as: G n [ g ( t ) ] s = , ∫ 0 ∞ − 1 e d > . We prove some properties and give examples. Also, applications are given.

This article demonstrates how the new Double Laplace–Sumudu transform (DLST) is successfully implemented in combination with iterative method to obtain exact solutions of nonlinear partial differential equations (NLPDEs) by considering specified conditions. The terms these were determined using successive procedure. proposed technique has advantage generating solutions, and it easy apply analytically on given problems. In addition, theorems handling mode properties DLST have been proved. To...

In this article, the numerical adaptive predictor corrector (Apc-ABM) method is presented to solve generalized Caputo fractional initial value problems. The Apc-ABM was utilized establish approximate series solutions. technique considered be an extension original Adams–Bashforth–Moulton approach. Numerical simulations and figures are discussed, in order show efficiency of proposed method. future, we anticipate that provided derivative suggested will create simulate a wide variety Caputo-type...

In this research, a new approach for solving fractional initial value problems is presented. The main goal of study focuses on establishing direct formulas to find the coefficients approximate series solutions target problems. method provides analytical both and ordinary differential equations or systems directly, without complicated computations. To show reliability efficiency presented technique, interesting examples linear nonlinear orders are solved directly by approach. This faster...

This article presents the solution of fractional SIR epidemic model using Laplace residual power series method. We introduce in sense Caputo's derivative, it is presented by three differential equations, which third one depends on first coupled equations. The method implemented this research to solve proposed model, we present a form convergent expansion that converges rapidly exact one. analyze results and compare obtained approximate solutions those from other methods. Figures tables are...

The subject of this study is the solution a fractional Bernoulli equation and chaotic system by using novel scheme for derivative comparison approximate exact solutions. It found that suggested method produces solutions are identical to solution. We can therefore generalize strategy different systems get more accurate results. think has been offered algorithm will be utilized in future construct simulate variety models used solve difficult physics engineering challenges.

Abstract Non-uniform heat sources and sinks are used to control the temperature of reaction ensure that it proceeds at desired rate. It is worldwide in nature may be found all engineering applications such as nuclear reactors, electronic devices, chemical etc . In food processing, cook microwave ovens, pasteurize infrared heaters, sterilize products. mainly biomedical applications, hyperthermia cancer treatment, target kill cells. Because its ubiquitous nature, idea taken our subject study....

Abstract Many applications, including micro air vehicles, automotive, aerospace, refrigeration, mechanical–electromechanical systems, electronic device cooling, and heat exchanger can be used to determine the flow in microchannels. Regarding engineering optimization discusses role of entropy production minimization. Therefore, this work explores new facets fully developed Carreau fluid transport an inclined microchannel considering exponential space/temperature dependence, radiative flux,...

The fundamental goal of this research is to suggest a novel mathematical operator for modeling visceral leishmaniasis, specifically the Caputo fractional-order derivative. By utilizing Fractional Euler Method, we were able simulate dynamics fractional leishmaniasis model, evaluate stability equilibrium point, and devise treatment strategy disease. endemic disease-free points are studied as symmetrical components proposed dynamical together with their stabilities. It was shown that calculus...

The COVID-19 pandemic has exerted a pervasive worldwide influence, including on South Africa, which stands out as one of the African nations most substantially impacted. As March 20, 2021, nation encountered multitude obstacles in its efforts to contain virus's transmission. Conventional approaches forecasting transmission contagious illnesses frequently prove inadequate when it comes comprehending intricate dynamics COVID-19, specifically with regard stochastic disruptions and efficacy...

This paper explores the controllability of nonlocal intuitionistic fuzzy integro-differential equations using semigroups and contraction mapping principle. By establishing a clear theoretical approach, we show that it is possible to achieve under specific conditions. study offers new methods significant insights into analysis systems. The results demonstrate that, given right conditions, controlling systems with features feasible, addressing important challenges in this area.

In this article a new approach in solving time fractional partial differential equations is introduced, that is, the ARA-residual power series method. The main idea of technique, depends on applying ARA-transform and using Taylor's expansion to construct approximate solutions. procedure getting solutions for nonlinear difficult mission, method over comes trouble throughout expressing solution form then obtain coefficients residual function concept limit at infinity. This efficient applicable...

The main purpose of this work is to present a new double transform called the ARA-Sumudu (DARA-ST). application some basic functions and master properties are introduced. convolution existence theorems also presented proved. These results implemented obtain solution partial differential equations (PDEs), integral (IEs) functional equations. We formulas for solving families PDEs. latter ones used exact solutions familiar PDEs such as telegraph equation, advection–diffusion Klein–Gordon...

In this article, we apply the double ARA–Sumudu transformation (DARA-ST) to nonlocal fractional Caputo derivative operator. We achieve interesting results and implement them solve certain classes of partial differential equations (FPDEs). Several physical applications are discussed analyzed, such as telegraph, Klein–Gordon Fokker–Planck equations. The new technique with DARA-ST is efficient accurate in examining exact solutions FPDEs. order show applicability presented method, some numerical...

The objective of this work is to investigate analytical solutions some models cancer tumors using the Laplace residual power series method (LRPSM). proposed was effective and required simple calculations find analytic solution, utilizing computer software such as Mathematica package. Figures graphs attained Maclaurin are presented depict procedure. outcomes we obtained in research showed applicability strength approach studying numerical differential equations fractional orders.

<abstract> <p>In this paper, we introduce a new technique, called the direct power series method to solve several types of time-fractional partial differential equations and systems, in terms Caputo derivative. We illustrate with simple algorithm that can be used different problems. theorem explain required substitutions proposed method. In addition, convergence analysis conditions are given. Furthermore, some illustrative examples systems discussed show applicability simplicity...

In this research, systems of linear and nonlinear differential equations fractional order are solved analytically using the novel interesting method: ARA- Residual Power Series (ARA-RPS) technique. This approach technique is based on combination residual power series scheme with ARA transform to establish analytical approximate solutions in a fast convergent representation concept limit. The proposed method needs less time effort compared To prove simplicity, applicability, reliability...

<abstract> <p>In this research, a hybrid method, entitled the Laplace Residual Power Series technique, is adapted to find series solutions time-fractional model of Navier-Stokes equations in sense Caputo derivative. We employ proposed method construct analytical target problem using idea transform and residual function with concept limit at infinity. A simple modification suggested presented deal easily nonlinear terms constructed on properties power series. Three interesting...

Many formulas of improper integrals are shown every day and need to be solved in different areas science engineering. Some them can solved, others require approximate solutions or computer software. The main purpose this research is present new fundamental theorems that generate tables integrals. We six with associated remarks viewed as generalizations Cauchy’s results I.S. Gradshteyn integral tables. Applications difficult problems presented cannot the usual techniques residue contour...