Advances in Mathematical Modelling, Applied Analysis and Computation

Based on trigonometric and hyperbolic Taylor’s type formulae we establish related Shisha-Mond form inequalities leading to interesting Korovkin theorems. We deal with the high order of approximation of positive linear operators to the unit operator. The results are quantitative via the modulus of continuity. We finish with applications to Bernstein operators.

In this paper, we investigate the bicomplex Schrödinger’s equation of fractional order and derive its solution via Euler identity. The first order time derivative of the bicomplex Schrödinger’s equation is changed into a Caputo fractional derivative, resulting in the time fractional Schrödinger’s equation. The Euler identity for the bicomplex Mittag-Leffler function has been established and is being utilized to solve the bicomplex time fractional Schrödinger’s equation. The bicomplex time fractional Schrödinger equation is solved for a free particle and a potential well and the answer is represented in terms of the bicomplex Mittag-Leffler function. There are both hyperbolic and complex numbers in the bicomplex numbers. Through research in the bicomplex space, the results that are created independently for these can be brought together.

In 1945, Kaplansky [4] introduced the concept of the games being completely mixed and presented a necessary and sufficient condition for a game associated with a skew-symmetric matrix to be completely mixed. Recently, we have provided an additional condition for such games. It is known that skew symmetric matrices are \(Q_0\) and \(P_0\). In 1997, Murthy and Parthasarathy proved that if a matrix B belongs to fully copositive (\(C_0^f\)) and \(Q_0\), then B also belongs to \(P_0\). Building upon these results, our main result states that if the game associated with a fully copositive \(Q_0\)-matrix B is completely mixed, then \(B + D_j \in Q\) for all j from 1 to n, where \(D_j\) is a diagonal matrix whose \(j^{th}\) diagonal entry is 1 and else 0. Additionally, we prove that if \(B \in C^f_0 \cap Q_0\) but not a Q-matrix, then \(G_B\) is completely mixed game if and only if \(B + D_j \in Q\) for all j from 1 to n.

To propose the computational method for obtaining the numerical solutions for Riccati differential equations is the primary focus of this work. Riccati differential equations are important because they are applicable to a wide range of physical and engineering phenomena. Riccati differential equations are still extremely difficult to solve using conventional or contemporary numerical methods due to their inherent nonlinearity. By applying the basic ideas of Vieta-Fibonacci wavelets, this study presents an artificial neural network based method for effectively solving the nonlinear Riccati differential equations. In addition, the problem is solved using a single-layer functional link neural network. The proposed numerical method is applied to solve various cases of Riccati differential models. The obtained numerical results indicate a higher level of congruence between the approximate and exact values, proving the accuracy and efficiency of the proposed method.

Diabetes is one of the most common illnesses internists encounter and an emerging global health problem. This is because the lifestyle of people today is sedentary and lacks the nutrition required in their diet. To prevent this, we need an optimal diet model. Accordingly, to the experts, the low-calorie diet having high starch carbohydrates, high fiber, and low fat is the best way to treat diabetes. Consequently, the proposed model is a multiobjective linear programming model with the maximization of fiber and carbohydrates and the minimization of fat and sugar. The constraints are daily maximum to minimum nutrient requirements of carbohydrates, fat, fiber, and sugar. But in most studies, the daily nutrient intake decisions were made based on crisp data. By prescribing a diet based on crisp data, some of the realities are neglected. Furthermore, establishing a precise threshold for the upper and lower limits of individuals’ daily nutrient intake is challenging due to various factors including geographical location, gender, age, and the inherent variability and lack of clarity in nutrient use. The fuzzy concept can best represent obscurity. But the fuzzy concepts can represent only the chance of a healthy diet acceptance and what if the chance of diet is not healthy is non-acceptance. Hence Intuitionistic fuzzy sets are employed for the acceptance and non-acceptance of nutrients in a diabetic diet. So both the objective and set of constraints are intuitionistic fuzzy sets. A numerical example illustrates the diet model under an intuitionistic fuzzy environment. The findings show that the degree of acceptance of various daily nutrients in a diabetic diet is 97% and rejection 29% for the age group between 35 to 45 years.

We propose the t-norm of the doubt Q-fuzzy T-subalgebra and the T-ideal of the BP-algebra, and investigate some of their properties in this work. In addition, we define properties of Cartesian products of doubt Q-fuzzy T subalgebras and T-ideals of BP algebras. These are treated in detail along with other algebraic properties.

Quadcopters play a vital role in various industries due to their excellent maneuverability, enabling them to access hard-to-reach areas and perform tasks that traditional aircraft or vehicles cannot accomplish. The Quadcopter has 6-DoF movements that include both linear (x, y, z) and angular (roll, pitch, and yaw angles) motions. The study explores a new approach to study Quadcopter movement through the integration of Computational Fluid Dynamics, and proportional-integral-derivative with Numerical Methods. This work is useful to design a control system for the stability and maneuverability of quad-copter motion.

In the present work, we developed mathematical models for quadcopter movement, simulated the models, and validated them using data from previous research. Our study is valuable for aviation system automation.

The present work uses both nonlinear and linear methods to investigate how the instability of micropolar nanofluid inside Hele-Shaw cells is affected by magnetic field modulation. For nonlinear stability, the truncated Fourier series methodology is utilised, while for linear stability, the normal mode method is employed for analytical study. The results are all represented graphically. The findings show that the system is stabilised by the micropolar parameter, magnetic Chandrasekhar number, Hele-Shaw number, and the coefficient of coupling between vorticity and spin effect. Contrarily, The beginning of convective motion inside the system is accelerated by the nanoparticle Rayleigh number. Certain parameters have a major impact on the heat/mass transfer in non-linear analysis. The system’s mass transfer (MT) and heat transfer (HT) are significantly influenced by the magnetic Chandrasekhar number, micropolar parameter, Hele-Shaw number, and magnetic Prandtl number. In microfluidic applications, Hele-Shaw cells can be designed to study heat/mass transfer at small scales. The cell can be employed to investigate convective heat transfer.

Studies of real life market practices reveal that, large pile of consumer products are showcased in a retail outlet to promote sales and profits. This paper intends to develop an EOQ model incorporating different payment schemes for items withessing stock dependent demand. While procuring an item, the procurer might follow any of these payment methods: paying advance while booking the order or cash on delivery or paying at the end of an interest free credit period. As per the perspective of a supply chain member, each of these methods have pros and cons associated with it. In a real life scenario, one usually uses a payment scheme which is an amalgamation of the above mentioned methods. The proposed model presents a replenishment scheme for trader/retailer who has items with stock dependent demand and wants to observe a combination of different payment schemes. The trader/retailer implements an advance-cash-credit payment stratagem to procure items and practices cash-credit payment scheme while selling. The model is validated using numerical examples with pertinent values of inventory parameters; additionally, sensitivity analysis is done to yield managerial insights on the proposed model.

The new virus, COVID-19, spread quickly throughout Wuhan, China, other regions of China, and adjacent countries after the first case of unknown origin surfaced at Jinyintan Hospital in Wuhan, China, in December 2019. We developed epidemiological models and time models to estimate the incidence and short-term spread of COVID-19. This will enable institutions at all levels in China to respond and prevent COVID-19, while freeing up more time for clinical research. In the SIR and SI model, the main reproduction number is calculated analytically. The new generation matrix allows us to calculate the initial production number \(R_0\) according to the SEIR corona model, and the results show that with \(R_01\) the coronavirus does not spread in the body, but with \(R_0\) cannot less then 1. The disease will spread throughout society. The overall sensitivity and adaptability of the critical number of births are examined. Prevention and contamination are also covered and we use simple print codes as a guide. We analyzed past epidemic models such as West Nile virus and Zika virus using the next-generation matrix. Finally, we examined two coronavirus samples and determined the production number. It turns out that the distinction does not matter when the system is clogged. However, if the isolation rate is above the critical value, infection will not occur in the community. We showed the daily spread of coronavirus using some data.

Elliptic-type integrals (ETIs) are very useful in solving many problems related to radiation and nuclear physics. Previously, Many authors have worked on the unification and generalization of ETIs. This work aims to derive some new theorems on generating functions. Further, we derive some more new and known results on Euler-type integrals with the help of incomplete H functions (IHFs), incomplete \(\bar{H}\) functions (I\(\bar{H}\)Fs) and generating functions.

Medical image fusion plays a critical role in enhancing diagnostic accuracy and the clinical decision-making process by combining information from multiple medical imaging modalities. Transform domain techniques have shown promising results in medical image fusion, as they effectively capture the transform-based information present in the images. This paper presents a comprehensive comparative study of medical image fusion using different transform domain techniques. Each technique is applied to diverse medical images, such as MRI, CT, and PET, representing different anatomical structures and pathological conditions. For each transform domain technique, we analyze the fusion process, including decomposition, fusion rules, and reconstruction. The computational complexity of each algorithm and performance evaluation is conducted using objective fusion metrics with the help of MATLAB software. Furthermore, we evaluate the robustness of the techniques under varying noise levels, image artifacts, and fusion parameters. Our experimental results reveal that each transform domain technique has its strengths and limitations, depending on the specific imaging modality and clinical application. Overall, this comparative study contributes to medical image fusion research advancement, guiding researchers and practitioners in choosing the most suitable transform domain technique for enhancing medical image interpretation, disease diagnosis, and treatment planning.

Robotics has become an interesting field of study in the automation of agricultural practices. Currently, various robots have been made available for industrial applications. In light of the growing importance of agriculture, there has been an increasing demand for robots that can efficiently perform agricultural tasks while significantly reducing task completion time. This article addresses this need by presenting the design and development of a mathematical model for a novel SCARA robot to perform some agricultural tasks such as weed detection and removal, and planting.

An ordinary SCARA robot is fixed in a place and performs work using its arm, which is divided into shoulder and elbow movements. The movement of the SCARA robot depends upon accurate estimation of shoulder and elbow joint angles and the size of the shoulder and elbow. We enhanced the ordinary SCARA robot by adding an additional SCARA arm, and both SCARA arms are fixed on a movable vehicle. This proposed type of robot is transportable in an agricultural field.

In the present article, we develop a mathematical model for the proposed robot that is capable of moving in an agricultural field and performing tasks such as weed detection and removal, and planting. The proposed work is helpful for the design and development of a robotic system to perform agricultural tasks.

A mathematical model has been developed to describe the controlled drug distribution from drug-eluting stents into the arteries. This model includes the polymer layer, adventitial layer and diffusion front. A mathematical model for the fractional diffusion equation is developed using the Homotopy Perturbation Method. Results show that this method produces a drug concentration profile and a fractional release rate in the polymer matrix (first layer). The current study provides a systematic method for improving medication flow by increasing the parameters \(\eta \) and \(\alpha \) (fractional derivative).

The generalized hypergeometric functions of one, two and more variables and allied Special Functions, and their associated transformations, reductions and summations are potentially useful, not only as solutions of ordinary and partial differential equations, but also in the widespread problems in the mathematical, physical, engineering, and statistical sciences. In the same context, by applying two well-known Euler’s transformations for the Gauss hypergeometric function, Liu and Wang, in 2014, established five general double series transformations involving some appropriately bounded sequences of complex numbers, and used the derived results to deduce many additional transformations, reductions and summations for the Kampé de Fériet function. The main objective of this work is to provide an essential and convenient methodology to prove, the five general transformations due to Liu and Wang, by applying the classical hypergeometric summation theorems. Motivated from the developed methodology, numerous additional general double series transformations involving some appropriately bounded sequences of complex numbers, are investigated. It is also shown that the newly obtained transformations, not only contain the five general transformations due to Liu and Wang but also lead to many other additional transformations and reductions for the Kampé de Fériet and the Srivastava-Daoust type double hypergeometric series. Further special cases are also examined.

Analyzing the interactions among three species within a food chain is made possible by utilizing a tri-trophic food chain model based on the Leslie-Gower framework. As a result of introducing alternative food into the system, the model can be used to examine the potential impact of chaos on the occurrence and control of chaos. Alternative food introductions can contribute to or control chaos depending on how readily available and nutritionally valuable they are. In addition to reducing the pressure on resource species, alternative food sources can reduce chaos if they are abundant and nutritious. It is possible, however, that the introduction of alternative food can lead to overexploitation of resource species and chaos if the alternative food source is not as nutritious or abundant. Additionally, the introduction of alternative food can affect the dynamics of primary consumers and top predators. The Leslie-Gower-type tritrophic food chain model provides insight into alternative food’s role in causing and controlling chaos in food chains.

Balamurugan et al. introduced the notion of anti-intuitionistic fuzzy soft ideals in BCK/BCI-algebras [5] and Muhiuddin et al. introduced Anti-Intuitionistic Fuzzy Soft a-Ideals applied to BCI-Algebras [13]. In this article, the notion of anti-intuitionistic fuzzy soft modules in BCK/BCI-algebras has been introduced and some of their properties have been discussed.

This paper introduces an innovative cubic B-spline method designed for computing precise numerical solutions to linear partial differential equations in one dimension. Through a comprehensive error analysis, the proposed technique has been extensively evaluated, showcasing its robust stability. Its application across diverse convection-diffusion linear problems-encompassing fields such as heat transfer, acoustics, and mass transfer-has proven its efficacy and accuracy. Comparative assessments against exact solutions have highlighted the superiority of our method, consistently delivering improved numerical outcomes.

In this chapter, we discuss one of the recent generalization of Schwartz distributions that has significantly influenced the expansion of various mathematical disciplines. Here, we study the space of generalized quotient on the torus. Different integral transforms are investigated on the space of generalized quotients on the torus \(\mathcal {B}_{\mathcal {S}^{\prime }}(T^{d})\). The space \(\mathcal {B}_{\mathcal {S}^{\prime }}(T^{d})\) is made of both distributions as well as space of hyperfunctions on the torus. Further, by introducing the relation between the Fourier and other integral transforms, the conditional theorems are proved for generalized quotients on tours. Moreover, we study the convergence structure of delta-convergence on the generalized quotient space, and an inversion theorem is proved.

Effect of the couple-stress on micro polar fluid layer heated from below in a porous medium is studied. The dispersion relation was obtained using the normal mode and the problem has been numerically analyzed by MATLAB. The effect of permeability, couple-stress parameter, magnetic field and micro-polar parameters have been obtained and the effect of magnetic field on the system is very important result. The condition of over stability is also obtained.

Imagine solving a labyrinthine environmental maze: how to transport goods sustainably. This study focuses on an innovative approach to solving the challenge of environmentally friendly goods transportation within an endurable supply chain. It addresses the complex Fractional Solid Transportation Problem by integrating Neutrosophic Goal Programming techniques. This method efficiently deals with uncertain information in optimization, considering goals, constraints, and decision variables with varying degrees of truth, indeterminacy, and falsity. The primary aim is to optimize the distribution of goods to a green supplier, emphasizing fractional solid transportation. This problem arises in scenarios like resource distribution, supply chain management, and network flow optimization, all with a common goal of minimizing environmental impact. The proposed model effectively combines fractional solid transportation with Neutrosophic Goal Programming to manage conflicting objectives. The model incorporates real-world uncertainties through neutrosophic sets, allowing for a comprehensive representation of conflicting goals. Weight factors are introduced to prioritize objectives, enabling decision-makers to tailor trade-offs between different goals. Neutrosophic Goal Programming utilizes these weights to balance goals and constraints considering varying degrees of truth and uncertainty, guiding the optimization process effectively. Numerical experiments demonstrate the model's efficacy in handling the complexities of the fractional solid transportation problem, aiding sustainable decision-making in supply chain management. Unveil the treasure map of optimization, where each solution is a piece waiting to be placed, and the ranking approach is the compass guiding us to the best optimal solution. Furthermore, it can be implemented with optimization software such as Lingo 18, which provides a powerful computational tool to make these eco-friendly logistics a reality and effectively prioritize eco-conscious decision-making. This innovative approach could revolutionize eco-friendly logistics, offering a strategic method to transport goods sustainably while adhering to environmentally conscious principles.

In the present article, we investigate the impact of gravity modulation and through-flow on the instability of magneto-convection in a rotating layer of nano-liquid. Compared to regular liquids, nano-liquids have significantly better heat transmission efficiency, and therefore they can work as excellent coolants in various industries where cooling is a challenge. The normal mode technique and a two-term Fourier series expression have been applied for linear and non-linear exploration, respectively. In linear analysis, we found the impact of many parameters on the initiation of convection. Through-flow has a dual impact on the system. The magnetic Chandrasekhar number and the Taylor number both have stabilizing effects. The magnetic Prandtl number does not affect the initiation of convection. With the use of Mathematica NDSolve and the RKF-45, the rate of heat and mass movement in the area was examined. It was discovered that the rate is identical in both scenarios. Thus, the RKF-45 approach proved the convergent nature of all Mathematica NDSolve solutions. In a nonlinear study, the influence of through-flow, magnetic Chandrasekhar number, Taylor number, the frequency of G-jitter, and the amplitude of G-jitter on heat and mass transport is investigated. The heat and mass transportation increase while the growth of the through-flow. As the MC (Magnetic Chandrasekhar) number and Taylor number increase, the heat and mass transportation in the domain decrease.

The approximate solutions for the two dimensional nonlinear PDEs with Liouville-Caputo fractional derivative are determined and presented in this paper. Comparative numerical simulations obtained from alternative models are introduced in order to demonstrate the effectiveness and precision of the proposed techniques. Various source terms are taken into account in the fractional nonlinear differential equations. It is shown that the classical behaviors are restored in case that the fractional order \(\alpha \) is equal to 1.

In addition to its ability to handle complex uncertain information, dual Hesitant Fermatean fuzzy sets (DHFFS) can be used to solve a wider range of multi-criteria decision making (MCDM) problems. To achieve our goal, we first proposed a score function for the ranking of DHFFS and thereafter we employed the proposed operations to develop DHFF information based hamacher average and geometric aggregation operators with their specific cases. After that, we utilize aforementioned operators to create a methodology for addressing real-world MCDM challenges. To emphasize the importance of proposed methods, a study based on the evaluation of sustainability of healthcare systems is conducted.