Probabilistic Forecasting of Electricity Demand Incorporating Mobility Data

Due to extreme weather conditions and anomalous events such as the COVID-19 pandemic, utilities and grid operators worldwide face unprecedented challenges. These unanticipated changes in trends introduce new uncertainties in conventional short-term electricity demand forecasting (EDF) since its result depends on recent usage as an input variable. In order to quantify the uncertainty of EDF effectively, this paper proposes a comprehensive probabilistic EFD method based on Gaussian process regression (GPR) and kernel density estimation (KDE). GPR is a non-parametric method based on Bayesian theory, which can handle the uncertainties in EDF using limited data. Mobility data is incorporated to manage uncertainty and pattern changes and increase forecasting model scalability. This study first performs a correlation study for feature selection that comprises weather, renewable and non-renewable energy, and mobility data. Then, different kernel functions of GPR are compared, and the optimal function is recommended for real applications. Finally, real data are used to validate the effectiveness of the proposed model and are elaborated with three scenarios. Comparison results with other conventional adopted methods show that the proposed method can achieve high forecasting accuracy with a minimum quantity of data while addressing forecasting uncertainty, thus improving decision-making.

Post-Pandemic Sector-Based Investment Model Using Generalized Liouville–Caputo Type

In this article, Euler's technique was employed to solve the novel post-pandemic sector-based investment mathematical model. The solution was established within the framework of the new generalized Caputo-type fractional derivative for the system under consideration that serves as an example of the investment model. The mathematical investment model consists of a system of four fractional-order nonlinear differential equations of the generalized Liouville–Caputo type. Moreover, the existence and uniqueness of solutions for the above fractional order model under pandemic situations were investigated using the well-known Schauder and Banach fixed-point theorem technique. The stability analysis in the context of Ulam—Hyers and generalized Ulam—Hyers criteria was also discussed. Using the investment model under consideration, a new analysis was conducted. Figures that depict the behavior of the classes of the projected model were used to discuss the obtained results. The demonstrated results of the employed technique are extremely emphatic and simple to apply to the system of non-linear equations. When a generalized Liouville–Caputo fractional derivative parameter (ρ) is changed, the results are asymmetric. The current work can attest to the novel generalized Caputo-type fractional operator's suitability for use in mathematical epidemiology and real-world problems towards the future pandemic circumstances.

Numerical Simulation for a Hybrid Variable-Order Multi-Vaccination COVID-19 Mathematical Model

In this paper, a hybrid variable-order mathematical model for multi-vaccination COVID-19 is analyzed. The hybrid variable-order derivative is defined as a linear combination of the variable-order integral of Riemann–Liouville and the variable-order Caputo derivative. A symmetry parameter σ is presented in order to be consistent with the physical model problem. The existence, uniqueness, boundedness and positivity of the proposed model are given. Moreover, the stability of the proposed model is discussed. The theta finite difference method with the discretization of the hybrid variable-order operator is developed for solving numerically the model problem. This method can be explicit or fully implicit with a large stability region depending on values of the factor Θ. The convergence and stability analysis of the proposed method are proved. Moreover, the fourth order generalized Runge–Kutta method is also used to study the proposed model. Comparative studies and numerical examples are presented. We found that the proposed model is also more general than the model in the previous study;the results obtained by the proposed method are more stable than previous research in this area.

Fractional Optimal Control Model of SARS-CoV-2 (COVID-19) Disease in Ghana

Research focus on optimal control problems brought on by fractional differential equations has been extensively applied in practice. However, because they are still open ended and challenging, a number of problems with fractional mathematical modeling and problems with optimal control require additional study. Using fractional-order derivatives defined in the Atangana–Baleanu–Caputo sense, we alter the integer-order model that has been proposed in the literature. We prove the solution's existence, uniqueness, equilibrium points, fundamental reproduction number, and local stability of the equilibrium points. The operator's numerical approach was put into practice to obtain a numerical simulation to back up the analytical conclusions. Fractional optimum controls were incorporated into the model to identify the most efficient intervention strategies for controlling the disease. Utilizing actual data from Ghana for the months of March 2020 to March 2021, the model is validated. The simulation's results show that the fractional operator significantly affected each compartment and that the incidence rate of the population rose when v≥0.6. The examination of the most effective control technique discovered that social exclusion and vaccination were both very effective methods for halting the development of the illness.

A Mathematical Model of the Risk Assessment for Airborne Transmission in a Classroom with a Ventilation System and Nine Distinct Face Mask Efficiency

TB, COVID-19, MERS, and SARS are all serious infectious diseases that are transmitted by the air or aerosol via coughing, spitting, sneezing, speaking, or wounds. When restaurants and bars reopen and continue operations in some parts of the United States, the Centers for Disease Control and Prevention (CDC) gives the following suggestions for how operators can reduce risk for employees, customers, and communities while also restricting the spread of COVID-19. The more and longer a person interacts with others, the greater the risk of COVID-19 spreading. Therefore, we need to be informed of its management and treatment. As a result, for the control and reduction of potentially polluted air, such as CO2 levels, good air quality management is required. They investigated the protective effectiveness of face masks against airborne transmission of infectious SARS-CoV-2 droplets and aerosols in response to the World Health Organization's recommendation to wear face masks to prevent the spread of COVID-19. Using nine different forms of mask efficiency, this research provides a mathematical model for calculating the chance of airborne transmission in a classroom. The fourthorder Runge-Kutta approach is used to approximate the model solution. The proposed strategy strikes a balance between the number of students allowed to stay in the classroom and the effectiveness of nine different masks. We can see how utilizing nine different masks and a well-ventilated system in the classroom can help to reduce the risk of airborne infection.

Fractional type multivariate neural network operators

In this paper, we introduce a novel family of multivariate neural network operators involving Riemann‐Liouville fractional integral operator of order α. Their pointwise and uniform approximation results are presented, and new results concerning the rate of convergence in terms of the modulus of continuity are estimated. Moreover, several graphical and numerical results are presented to demonstrate the accuracy, applicability, and efficiency of the operators through special activation functions. Finally, an illustrative real‐world example on the recent trend of novel corona virus Covid‐19 has been investigated in order to demonstrate the modeling capabilities of the proposed neural network operators.

Solving Optimization Problems Using an Extended Gradient-Based Optimizer

This paper proposes an improved method for solving diverse optimization problems called EGBO. The EGBO stands for the extended gradient-based optimizer, which improves the local search of the standard version of the gradient-based optimizer (GBO) using expanded and narrowed exploration behaviors. This improvement aims to increase the ability of the GBO to explore a wide area in the search domain for the giving problems. In this regard, the local escaping operator of the GBO is modified to apply the expanded and narrowed exploration behaviors. The effectiveness of the EGBO is evaluated using global optimization functions, namely CEC2019 and twelve benchmark feature selection datasets. The results are analyzed and compared to a set of well-known optimization methods using six performance measures, such as the fitness function's average, minimum, maximum, and standard deviations, and the computation time. The EGBO shows promising results in terms of performance measures, solving global optimization problems, recording highlight accuracies when selecting significant features, and outperforming the compared methods and the standard version of the GBO.

Fermatean Cubic Fuzzy Aggregation Operators and Their Application in Multiattribute Decision-Making Problems

The purpose of aggregation methods is to convert a list of objects of a set into a single object of the same set usually by an n-arry function, so-called aggregation operator. The key features of this work are the aggregation operators, because they are based on a novel set called Fermatean cubic fuzzy set (F-CFS). F-CFS has greater spatial scope and can deal with more ambiguous situations where other fuzzy set extensions fail to support them. For this purpose, the notion of F-CFS is defined. F-CFS is the transformation of intuitionistic cubic fuzzy set (I-CFS), Pythagorean cubic fuzzy set (P-CFS), interval-valued cubic fuzzy set, and basic orthopair fuzzy set and is grounded on the constraint that "the cube of the supremum of membership plus nonmembership degree is ≤1”. We have analyzed some properties of Fermatean cubic fuzzy numbers (F-CFNs) as they are the alteration of basic properties of I-CFS and P-CFS. We also have defined the score and deviation degrees of F-CFNs. Moreover, the distance measuring function between two F-CFNs is defined which shows the space between two F-CFNs. Based on this notion, the aggregation operators namely Fermatean cubic fuzzy-weighted averaging operator (F-CFWA), Fermatean cubic fuzzy-weighted geometric operator (F-CFWG), Fermatean cubic fuzzy-ordered-weighted averaging operator (F-CFOWA), and Fermatean cubic fuzzy-ordered-weighted geometric operator (F-CFOWG) are developed. Furthermore, the notion is applied to multiattribute decision-making (MADM) problem in which we presented our objectives in the form of F-CFNs to show the effectiveness of the newly developed strategy.

Analysis on Infection Wave and Decay of Transmission Risk Based on Spatial SIR Model - Taking COVID Epidemic as an Example

Starting with the spatial SIR model, this paper gives the strict boundary conditions, and obtains two theorems in the process of infectious disease transmission through theoretical analysis. After that, the partial differential equations are transformed into ordinary differential equations by the method of traveling wave solution, and the solutions of infectious wave velocity and hypergeometric function are further derived. Beside local diffusion operator model, the paper also developed global transmission risk functions as convolution kernels and discovered their properties. The solution of the spatial infectious disease model is visualized by programming, and the influence of parameter changes on the solution is discussed. Finally, some variants of the model in special cases are given. This paper proves that under generalized assumption the three population densities of the spatial SIR model results at the origin cannot take extreme values at the same time, and when the infected density takes extreme values at the origin, the higher-order derivative of the infected density to the space is zero. The hypergeometric function method verifies the solution at infinity of the equations, and the above solution can be used to approximate when the distance from the infection source radius is large. In this paper, the discussion on the impact of the changes of several infectious disease parameters can inspire the methods of epidemic prevention and control.

Time-Leveled Hypersoft Matrix, Level Cuts, Operators, and COVID-19 Collective Patient Health State Ranking Model

This article is the first step to formulate such higher dimensional mathematical structures in the extended fuzzy set theory that includes time as a fundamental source of variation. To deal with such higher dimensional information, some modern data processing structures had to be built. Classical matrices (connecting equations and variables through rows and columns) are a limited approach to organizing higher dimensional data, composed of scattered information in numerous forms and vague appearances that differ on time levels. To extend the approach of organizing and classifying the higher dimensional information in terms of specific time levels, this unique plithogenic crisp time-leveled hypersoft-matrix (PCTLHS matrix) model is introduced. This hypersoft matrix has multiple parallel layers that describe parallel universes/realities/information on some specific time levels as a combined view of events. Furthermore, a specific kind of view of the matrix is described as a top view. According to this view, i-level cuts, sublevel cuts, and sub-sublevel cuts are introduced. These level cuts sort the clusters of information initially, subject-wise then attribute-wise, and finally time-wise. These level cuts are such matrix layers that focus on one required piece of information while allowing the variation of others, which is like viewing higher dimensional images in lower dimensions as a single layer of the PCTLHS matrix. In addition, some local aggregation operators are designed to unify i-level cuts. These local operators serve the purpose of unifying the material bodies of the universe. This means that all elements of the universe are fused and represented as a single body of matter, reflecting multiple attributes on different time planes. This is how the concept of a unified global matter (something like dark matter) is visualized. Finally, to describe the model in detail, a numerical example is constructed to organize and classify the states of patients with COVID-19.

Novel Numerical Estimates of the Pneumonia and Meningitis Epidemic Model via the Nonsingular Kernel with Optimal Analysis

In this article, we investigated a deterministic model of pneumonia-meningitis coinfection. Employing the Atangana–Baleanu fractional derivative operator in the Caputo framework, we analyze a seven-component approach based on ordinary differential equations (DEs). Furthermore, the invariant domain, disease-free as well as endemic equilibria, and the validity of the model’s potential results are all investigated. According to controller design evaluation and modelling, the modulation technique devised is effective in diminishing the proportion of incidences in various compartments. A fundamental reproducing value is generated by exploiting the next generation matrix to assess the properties of the equilibrium. The system’s reliability is further evaluated. Sensitivity analysis is used to classify the impact of each component on the spread or prevention of illness. Using simulation studies, the impacts of providing therapy have been determined. Additionally, modelling the appropriate configuration demonstrated that lowering the fractional order from 1 necessitates a rapid initiation of the specified control technique at the largest intensity achievable and retaining it for the bulk of the pandemic’s duration.

Interval-Valued Linear Diophantine Fuzzy Frank Aggregation Operators with Multi-Criteria Decision-Making

We introduce the notion of the interval-valued linear Diophantine fuzzy set, which is a generalized fuzzy model for providing more accurate information, particularly in emergency decision-making, with the help of intervals of membership grades and non-membership grades, as well as reference parameters that provide freedom to the decision makers to analyze multiple objects and alternatives in the universe. The accuracy of interval-valued linear Diophantine fuzzy numbers is analyzed using Frank operations. We first extend the Frank t-conorm and t-norm (FTcTn) to interval-valued linear Diophantine fuzzy information and then offer new operations such as the Frank product, Frank sum, Frank exponentiation, and Frank scalar multiplication. Based on these operations, we develop novel interval-valued linear Diophantine fuzzy aggregation operators (AOs), including the “interval-valued linear Diophantine fuzzy Frank weighted averaging operator and the interval-valued linear Diophantine fuzzy Frank weighted geometric operator”. We also demonstrate various features of these AOs and examine the interactions between the proposed AOs. FTcTns offer two significant advantages. Firstly, they function in the same way as algebraic, Einstein, and Hamacher t-conorms and t-norms. Secondly, they have an additional parameter that results in a more dynamic and reliable aggregation process, making them more effective than other general t-conorm and t-norm approaches. Furthermore, we use these operators to design a method for dealing with multi-criteria decision-making with IVLDFNs. Finally, a numerical case study of the novel carnivorous issue is shown as an application for emergency decision-making based on the proposed AOs. The purpose of this numerical example is to demonstrate the practicality and viability of the provided AOs.

A Study on Dynamics of CD4+ T-Cells under the Effect of HIV-1 Infection Based on a Mathematical Fractal-Fractional Model via the Adams-Bashforth Scheme and Newton Polynomials

In recent decades, AIDS has been one of the main challenges facing the medical community around the world. Due to the large human deaths of this disease, researchers have tried to study the dynamic behaviors of the infectious factor of this disease in the form of mathematical models in addition to clinical trials. In this paper, we study a new mathematical model in which the dynamics of CD4+ T-cells under the effect of HIV-1 infection are investigated in the context of a generalized fractal-fractional structure for the first time. The kernel of these new fractal-fractional operators is of the generalized Mittag-Leffler type. From an analytical point of view, we first derive some results on the existence theory and then the uniqueness criterion. After that, the stability of the given fractal-fractional system is reviewed under four different cases. Next, from a numerical point of view, we obtain two numerical algorithms for approximating the solutions of the system via the Adams-Bashforth method and Newton polynomials method. We simulate our results via these two algorithms and compare both of them. The numerical results reveal some stability and a situation of lacking a visible order in the early days of the disease dynamics when one uses the Newton polynomial.

Distributionally Robust Model and Metaheuristic Frame for Liner Ships Fleet Deployment

The container shipping industry market is very dynamic and demanding, economically, politically, legally, and financially. Considering the high cost of core assets, ever rising operating costs, and the volatility of demand and supply of cargo space, the result is an industry under enormous pressure to remain profitable and competitive. To maximize profits while maintaining service levels and ensuring the smooth flow of cargo, it is essential to make strategic decisions in a timely and optimal manner. Fleet deployment selection, which includes the profile of vessel hire, as well as their capacity and port rotation, is one of the most important strategic and tactical decisions container shipping operators must make. Bearing in mind that maritime business is inherently stochastic and uncertain, the key aims of this paper are to address the problem of fleet deployment under uncertain operating conditions, and to provide an integrated and optimized tool in the form of a mathematical model, metaheuristic algorithm, and computer program. Furthermore, this paper will show that the properties of the provided solutions exceed those offered in the literature so far. Such a solution will provide the shipping operator with a decision tool to best deploy its fleet in a way that responds more closely to real life situations and to meet the maximum demand for cargo space with minimal expense. The final goal is to minimize the operating costs while managing cargo flows and reducing the risks of unfulfilled customer demands.

Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach

In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier’s law and Fick’s law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, and Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.

Pythagorean probabilistic hesitant fuzzy aggregation operators and their application in decision-making

Purpose>This is mainly because the restrictive condition of intuitionistic hesitant fuzzy number (IHFN) is relaxed by the membership functions of Pythagorean probabilistic hesitant fuzzy number (PyPHFN), so the range of domain value of PyPHFN is greatly expanded. The paper aims to develop a novel decision-making technique based on aggregation operators under PyPHFNs. For this, the authors propose Algebraic operational laws using algebraic norm for PyPHFNs. Furthermore, a list of aggregation operators, namely Pythagorean probabilistic hesitant fuzzy weighted average (PyPHFWA) operator, Pythagorean probabilistic hesitant fuzzy weighted geometric (PyPHFWG) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted average (PyPHFOWA) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted geometric (PyPHFOWG) operator, Pythagorean probabilistic hesitant fuzzy hybrid weighted average (PyPHFHWA) operator and Pythagorean probabilistic hesitant fuzzy hybrid weighted geometric (PyPHFHWG) operator, are proposed based on the defined algebraic operational laws. Also, interesting properties of these aggregation operators are discussed in detail.Design/methodology/approach>PyPHFN is not only a generalization of the traditional IHFN, but also a more effective tool to deal with uncertain multi-attribute decision-making problems.Findings>In addition, the authors design the algorithm to handle the uncertainty in emergency decision-making issues. At last, a numerical case study of coronavirus disease 2019 (COVID-19) as an emergency decision-making is introduced to show the implementation and validity of the established technique. Besides, the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.Originality/value>Paper is original and not submitted elsewhere.

Archimedean t-Norm and t-Conorm-Based Aggregation Operators of HFNs, with the Approach of Improving Education

The aim of this paper is to develop the calculus of hesitant fuzzy numbers (HFNs), have been recently proposed as the newest extension of hesitant fuzzy sets. At first, based on the willingness of decision maker to each part of HFNs, a new method has been proposed to compare them. Then, several t-norm and t-conorm-based aggregation operators of HFNs, i.e., algebraic t-norm and t-conorm, Einstein t-norm and t-conorm, Hamacher t-norm and t-conorm, Frank t-norm and t-conorm have been defined, and some of their mathematical properties are also discussed. As the special cases of the above t-norm and t-conorm-based aggregation operators of HFNs, Archimedean t-norm and t-conorm-based HFN weighted averaging operator, Archimedean t-norm and t-conorm-based HFN weighted geometric operator, Archimedean t-norm and t-conorm-based HFN ordered weighted averaging operator, and Archimedean t-norm and t-conorm-based HFN ordered weighted geometric operator have been proposed. The new problem of improving the process of educational activities under the Covid-19 epidemic conditions, for instance, has been defined as a multi-attribute group decision-making (MAGDM) problem, in which students are its options, courses are its criteria, and teachers are members of the decision-making team. Then, the scores of final exams and teachers’ assessments merged together as HFNs, and a new method has been proposed based on the before mentioned operators to solve the resulting MAGDM problem. A numerical example, the results of which are also analyzed, is responsible for explaining what is proposed in this article. Finally, subsequent studies in this area are briefly stated.

Editorial for Special Issue “Fractional Calculus and Special Functions with Applications”

The study of fractional integrals and fractional derivatives has a long history, and they have many real-world applications due to their properties of interpolation between operators of integer order. In [2], Salem and Alghamdi considered a nonlinear sequential-type Caputo fractional ordinary differential equation on a finite interval, with nonlocal multi-point boundary conditions and an overall fractional order between 1 and 3. A comparative analysis was performed to compare the results achieved by using the M-derivative and by using the usual Caputo derivative with respect to t. In [7], Uçar et al. considered a system of first-order ordinary differential equations, which is used to model the effect of computer worms, and replaced the first-order derivatives with fractional derivatives of Atangana–Baleanu type to obtain a different system, which they studied using fixed-point and Laplace transform techniques to prove existence, uniqueness, and stability properties.