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In this study, we employ the effective iterative method to address the fractional Wu-Zhang Equation within the framework of the Caputo Derivative. The effective iterative method offers a practical approach to obtaining approximate solutions for fractional differential equations. We seek to provide insights into its solution and behavior by applying this method to the Wu-Zhang Equation. Through numerical analysis and the presentation of relevant tables and Figures, we demonstrate the accuracy and efficiency of this method in solving the fractional Wu-Zhang Equation. This research contributes to the understanding and solution of fractional-order differential equations and their applications in various scientific and engineering domains. [ABSTRACT FROM AUTHOR]

Carbon nanotubes (CNTs) influenced nanofluid is gaining popularity in the industry for solar energy and scratch heat exchanger applications. Consequently, this research focuses on evaluating the impact of nonlinear thermal radiation from a CNT-based nanofluid on an unsteady three-dimensional nonasymmetric Homann stagnant flux as a function of length and radius. CNTs have remarkable thermal physical properties that appear to be critical for nonlinear thermal transport. As a result, the nonlinear heat transfer properties of H2O composed of single or multiple wall CNTs are studied. The nanomaterial has a length and radius of approximately 3 nm ≤ L ≤ 7 0 nm and 1 0 nm ≤ R ≤ 4 0 nm. Partially differential equations with appropriate similarity transformations serve as a mathematical model for the process. The numerical solution of the simplified system of equations is achieved via the use of the well-known Runge–Kutta (RK) method in conjunction with the shooting approach. An effective way to show how a component affects velocity and temperature, skin frictions in both direction and Nusselt number are utilized in graphical representations. Increasing the unsteadiness parameter causes a reduction in the temperature profile and the velocity profile in both directions. As ε grows larger with ϕ , the skin friction in both directions decreases, while the Nusselt number profile grows larger. In addition, the variation in the Nusselt number is included in the tables, along with a comparison of the model without radiation to the model with radiation. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative optimization model employing fuzzy logic to address the challenge of minimizing variance while considering costs in the context of a two-stage stratified random sampling model with a randomized response approach. The proposed model leverages the alpha-cut technique to establish an optimal allocation strategy, making it possible to effectively manage the trade-off between cost constraints and variance reduction objectives. To illustrate the practical application of the model, we provide numerical examples, demonstrating its efficacy in real-world scenarios. This research contributes to the field by offering a comprehensive framework for decisionmakers to enhance the quality of data collection processes, particularly in situations where preserving respondent privacy is crucial. The integration of fuzzy logic and randomized response techniques presents a novel approach to addressing the inherent challenges of collecting sensitive information while maintaining data integrity and cost-efficiency. [ABSTRACT FROM AUTHOR]

The main features of scientific effort in physics and engineering are the development of models for various physical issues and the development of solutions. In this paper, we investigate the numerical solution of time-fractional non-linear dispersive K(m, n, 1) type equations using two innovative approaches: the homotopy perturbation transform method and Yang transform decomposition method. Our suggested approaches elegantly combine Yang transform, homotopy perturbation method (HPM) and adomian decomposition method (ADM). With the help of the Yang transform, we first convert the problem into its differential partner before using HPM to get the He's polynomials and ADM to get the Adomian polynomials, both of which are extremely effective supports for non-linear issues. In this case, Caputo sense is used for defining the fractional derivative. The derived solutions are shown in series form and converge quickly. To ensure the effectiveness and applicability of the proposed approaches, the examined problems were analyzed using various fractional orders. We analyze and demonstrate the validity and applicability of the solution approaches under consideration with given initial conditions. Two and three dimensional graphs reflect the outcomes that were attained. To verify the effectiveness of the strategies, numerical simulations are presented. The numerical outcomes demonstrate that only a small number of terms are required to arrive at an approximation that is exact, efficient, and trustworthy. The results of this study demonstrate that the studied methods are effective and strong in solving nonlinear differential equations that appear in science and technology. [ABSTRACT FROM AUTHOR]

It is essential for mathematicians, physicists, and engineers to construct fractional mathematical models for specific phenomena and develop numerical or analytical solutions for these models. In this work, we implement the natural decomposition approach with nonsingular kernel derivatives to investigate the solution of nonlinear fractional forced Korteweg–de Vries (FF-KdV) equation. We first investigate the FF-KdV equation under the Caputo–Fabrizio fractional derivative. The similar equations are then examined using the Atangana–Baleanu derivative. This approach combines the decomposition method with the Natural transform method. The series solution of the suggested equations is thus obtained using the natural transform. The key benefit of this novel approximate-analytical approach is that it may provide an analytical solution for the FF-KdV problem in the form of convergent series with simple computations. For each equation, three unique situations are chosen to demonstrate and test the viability of the proposed method. To guarantee the competence and dependability of the proposed method, the nature for various values of the Froude number F r have been provided. The present approach is also used to calculate solutions at various fractional orders. The approximate series solution's behavior for various fractional orders has been graphically displayed. The outcomes demonstrate that the methodology is simple to use and reliable when applied to numerous fractional differential equations. [ABSTRACT FROM AUTHOR]

The primary goal of this study is to create and characterise solitary wave solutions for the conformable Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equations (FCBWBKEs), a model that governs shallow water waves. Through wave transformations and the chain rule, the authors used the modified Extended Direct Algebraic Method (mEDAM) for transforming FCBWBKEs into a more manageable Nonlinear Ordinary Differential Equation (NODE). This accomplishment is particularly noteworthy because it surpasses the drawbacks linked to both the Caputo and Riemann–Liouville definitions in complying to the chain rule. The study uses visual representations such as 3D, 2D, and contour graphs to demonstrate the dynamic nature of solitary wave solutions. Furthermore, the investigation of diverse wave phenomena such as kinks, shock waves, periodic waves, and bell-shaped kink waves highlights the range of knowledge obtained in the study of shallow water wave behavior. Overall, this study introduces novel methodologies that produce valuable and consistent results for the problem under consideration. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear (1 + n) -dimensional generalized Camassa–Holm Kadomtsev–Petviashvili (g-CH-KP) equation is examined using Lie theory. Lie point symmetries of the equation are computed using MAPLE software and are generalized for the case of any dimension. Moreover, the equation is transformed into a nonlinear ordinary differential equation using the Abelian subalgebra. The nonlinear self-adjoint classification of the equation under consideration is accomplished with the help of which conservation laws for a particular dimension are calculated. Moreover, the new extended algebraic approach is used to compute a wide range of solitonic structures using different set of parameters. Graphic description of some specific applicable solutions for certain physical parameters is portrayed. [ABSTRACT FROM AUTHOR]

In this study, we used two unique approaches, namely the Yang transform decomposition method (YTDM) and the homotopy perturbation transform method (HPTM), to derive approximate analytical solutions for nonlinear time-fractional Zakharov–Kuznetsov equations (ZKEs). This framework demonstrated the behavior of weakly nonlinear ion-acoustic waves in plasma containing cold ions and hot isothermal electrons in the presence of a uniform magnetic flux. The density fraction and obliqueness of two compressive and rarefactive potentials are depicted. In the Liouville–Caputo sense, the fractional derivative is described. In these procedures, we first used the Yang transform to simplify the problems and then applied the decomposition and perturbation methods to obtain comprehensive results for the problems. The results of these methods also made clear the connections between the precise solutions to the issues under study. Illustrations of the reliability of the proposed techniques are provided. The results are clarified through graphs and tables. The reliability of the proposed procedures is demonstrated by illustrative examples. The proposed approaches are attractive, though these easy approaches may be time-consuming for solving diverse nonlinear fractional-order partial differential equations. [ABSTRACT FROM AUTHOR]

Fractional calculus is at this time an area where many models are still being developed, explored, and used in real-world applications in many branches of science and engineering where non-locality plays a key role. Although many wonderful discoveries have already been reported by researchers in important monographs and review articles, there is still a great deal of non-local phenomena that have not been studied and are only waiting to be explored. As a result, we can continually learn about new applications and aspects of fractional modelling. In this study, a precise and analytical method with non-singular kernel derivatives is used to solve the Caudrey–Dodd–Gibbon (CDG) model, a modification of the fifth-order KdV equation (fKdV). The fractional derivative is taken into account by the Caputo–Fabrizio (CF) derivative and the Atangana–Baleanu derivative in the Caputo sense (ABC). This model illustrates the propagation of magneto-acoustic, shallow-water, and gravity–capillary waves in a plasma medium. The dynamic behaviour of the acquired solutions has been represented in a number of two- and three-dimensional figures. A number of simulations are also performed to demonstrate how the resulting solutions physically behave with respect to fractional order. The significance of the current research is that new solutions are obtained by using a strong analytical approach. Utilizing a fractional derivative operator to solve equivalent models is another benefit of this approach. The results of the present work have similar aspects to the symmetry of partial differential equations. [ABSTRACT FROM AUTHOR]

It was Shiue who have introduced the Cesàro spaces and was later studied by various authors as cited in the text. In regard of this, the main structure of this paper is to study and interpret the new space of the form C(p) (F, θ) by employing lacunary sequences and sequences of strictly positive real numbers. Some basic interesting properties and inclusions relations will be determined. [ABSTRACT FROM AUTHOR]

The scenario of this article is to introduce the space Rts (p, ∆) based on a general Riesz sequence space. Its completeness property is derived and its linear isomorphism property with ℓ(p) is proved. The Köthe-dual property of the space Rts (p, ∆) is also derived. Furthermore, its basis is constructed and some characterization of infinite matrices are given. [ABSTRACT FROM AUTHOR]

In this paper, we define some new notion continuous random variables of fractional order. Also, some new generalized inequalities will be computed. [ABSTRACT FROM AUTHOR]

The structure of the Cesàro spaces were investigated by various authors as cited in the text. The scenario of this manuscript is to bring out the spaces ... We will study some of their basic topological properties and obtain some inclusion relations concerning these spaces. [ABSTRACT FROM AUTHOR]

The aim of this work is to develop the new techniques of sequences by employing the gamma function by introducing the space rq(Δpg, κ) of non-integral order. The completeness property concerning to this non-integral order space will be developed. Many interesting properties will be illustrated. [ABSTRACT FROM AUTHOR]

AbstractThe current study employs the Cattaneo–Christov diffusion law to analyze the thermal tendency of Maxwell nanomaterials flowing over an unsteady stretching sheet. Thermophoretic and Brownian diffusion aspects of nanosolids are incorporated to investigate thermal and nanoparticle’s concentration distribution. Through flow similarities, the governing PDEs (Partial Differential Equations) are articulated into a set of nonlinear ODEs (Ordinary Differential Equations). The homotopy analysis approach, a recognized semi-analytical technique, is implemented to solve these differential equations. Results are presented graphically, revealing that higher magnetic field strengths diminish the flowing field. Temperature and nanosolids concentration distributions escalate with increasing thermal and singular relaxation time phenomena. Furthermore, when nanoparticle concentration decreases and Brownian motion intensifies, the temperature field rises. It is also observed that heightened resistive heating enhances the fluid’s capability to carry thermal energy. Overall, this investigation sheds light on the intricate interplay between several factors influencing the thermal behavior of Maxwell nanomaterials over a stretching board, offering insights into their practical applications. [ABSTRACT FROM AUTHOR]

AbstractA hyperbolic tangent fluid model characterized by shear rate dependent viscosity together with the effects of hybrid nanoparticles, Brownian motion, thermo-diffusion, and Nield’s conditions, is utilized for thermal enhancement purpose. Five percent copper nanoparticles and twenty percent alumina nanoparticles are submerged into ethylene glycol with the parametric influence of tangent hyperbolic fluid to obtain the tangent hyperbolic hybrid nano suspension. Numerical solutions of the nondimensionalized conservation laws are found by the Keller-box method. The influence of various parametric factors on velocity, temperature, concentration, Nusselt number, and Sherwood number has been discussed. A constant Nusselt number is noted with the influence of Nield’s constraints. A 90% increase in thermal conductivity is achieved by dispersing 5% copper and 20% alumina nanoparticles into the ethylene glycol with the influence of hyperbolic tangent fluid. The error and convergence analysis of the numerical solution have been discussed, along with the validation of the obtained numerical results. [ABSTRACT FROM AUTHOR]