International Journal of Applied and Computational Mathematics

https://link.springer.com/journal/40819

List of Papers (Total 125)

Extensive Study of Modern Approaches Used in Identifying the Buckingham Potential

This paper presents two mathematical approaches of estimating unknown parameters of the Buckingham potential. Two functional forms of the potential was investigated owing to the complexities and difficulties arising from the original Buckingham potential. These complexities are due to the combination of both powers and an exponent in mathematical representation of the potential...

Analysis of MHD Fluid Flow and Heat Transfer Inside an Inclined Deformable Filter Chamber: Lie Group Method

This paper investigates MHD fluid flow and distribution of heat inside a filter chamber during a process of filtering particles from the fluid. A flow model of MHD viscous incompressible fluid inside a filter is studied to seek semi-analytical solutions which are analysed to find flow and heat dynamics that lead to optimal outflow (maximum filtrates) during filtration. Lie group...

A Theory for Covid-19 Testing to Save Both Resources and Time

In Los Angeles, at one point, the Covid-19 testing positivity rate was 6.25%, or one in sixteen. This translates to, on average, one in sixteen specimens testing positive and the vast majority testing negative. Usually, we run sixteen tests on sixteen specimens to identify the positive one(s). This process can be time consuming and expensive. Since a group of negative specimens...

A Generalized (3+1)-Dimensional Nonlinear Wave Equation in Liquid with Gas Bubbles: Symmetry Reductions; Exact Solutions; Conservation Laws

The analysis of a generalised (3+1)-dimensional nonlinear wave equation that simulates a variety of nonlinear processes that occur in liquids including gas bubbles will be performed. After some cosmetic adjustments to the underlying equation, this generalised (3+1)-dimensional nonlinear wave equation naturally degenerates into the (3+1)-dimensional Kadomtsev-Petviashvili equation...

Viscous Effect on Solitary Kelvin Wave in Open Cylindrical Channel under Precession

Viscous effect is introduced into the system of Navier–Stokes equations, that were derived to study the solitary Kelvin mode in an open cylindrical channel that precesses. Accordingly, three new weakly nonlinear models were derived: Korteweg–de Vries-Burgers, and two new Benjamin–Bona–Mahony-Burgers. The first was solved analytically by discussing the phase solution and...

Spatio-Temporal SIR Model with Robin Boundary Condition and Automatic Lockdown Policy

This paper presents the SIR space-time model, which is a coupled reaction–diffusion system with nonlinear Robin boundary conditions. These boundary conditions are supposed to lock the border (no outflow neither immigration nor migration) when the number of infected individuals explode, and this may be considered as an automatic containment or lock-down. In practice, we can...

Study of a Nonlinear System of Fractional Differential Equations with Deviated Arguments Via Adomian Decomposition Method

This paper studies a system of nonlinear fractional differential equations (FDEs) with deviated arguments. Many linear and nonlinear problems are faced in the real-life. Generally, linear problems are solved quickly, but some difficulties appear while solving nonlinear problems. Our purpose is to approximate those solutions numerically via the Adomian decomposition method (ADM...

Connectivity Concepts in Intuitionistic Fuzzy Incidence Graphs with Application

In this research article, we presented the idea of intuitionistic fuzzy incidence graphs (IFIGs) along with connectivity concepts. IFIGs are the generalization of fuzzy incidence graphs (FIGs). Specific ideas analogous to intuitionistic fuzzy cut-vertices and intuitionistic fuzzy bridges in intuitionistic fuzzy graphs, intuitionistic incidence cut-vertices, and intuitionistic...

An Efficient Numerical Scheme for Solving a Fractional-Order System of Delay Differential Equations

Fractional order systems of delay differential equations are very advantageous in analyzing the dynamics of various fields such as population dynamics, neural networking, ecology, and physiology. The aim of this paper is to present an implicit numerical scheme along with its error analysis to solve a fractional-order system of delay differential equations. The proposed method is...

Caputo Fractal Fractional Order Derivative of Soil Pollution Model Due to Industrial and Agrochemical

This paper narrates a non-linear and non-local Caputo fractal fractional operator of eco epidemic model with the advance of soil pollution considered in five compartments. The qualitative analysis of solutions such as existence and uniqueness of the model is carried out by using the standard condition of Schauder’s fixed point theorem and Banach Contraction principle. The local...

Study of Fractional Order SEIR Epidemic Model and Effect of Vaccination on the Spread of COVID-19

In this manuscript, a fractional order SEIR model with vaccination has been proposed. The positivity and boundedness of the solutions have been verified. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium point $${E}_{0}$$ when $${\mathfrak{R}}_{0}$$ < 1 and at epidemic equilibrium $${E}_{1...

Study of Results of Katugampola Fractional Derivative and Chebyshev Inequailities

In this work, we use generalized form of Caputo-type fractional derivative and Riemann–Liouville fractional Integral which is known as Katugampola fractional derivative. This work deals with some results having applications of Katugampola fractional derivative. We discuss commutative and inverse property of Katugampola fractional derivative. We have also introduced Chebyshev...

Comparative Study of the Fractional-Order Crime System as a Social Epidemic of the USA Scenario

Fractional derivatives are considered significant mathematical tools to design the fractional-order models of real phenomena. In this investigation, we are going to design and compare the non-integer models of the crime system by using three fractional-order operators called Atangana-Baleanu-Caputo, Caputo, and Caputo-Fabrizio derivatives for the first time. We use the real...

Numerical Solution of Two-Dimensional Time Fractional Mobile/Immobile Equation Using Explicit Group Methods

In this paper, we shall present the development of two explicit group schemes, namely, fractional explicit group (FEG) and modified fractional explicit group (MFEG) methods for solving the time fractional mobile/immobile equation in two space dimensions. The presented methods are formulated based on two Crank-Nicolson (C-N) finite difference schemes established at two different...

On Existence and Admissibility of Singular Solutions for Systems of Conservation Laws

A weak notion of solution for systems of conservation laws in one dimension is put forward. In the framework introduced here, it can be shown that the Cauchy problem for any $$n\times n$$ system of conservation laws has a solution. The solution concept is an extension of the notion of singular $$\delta $$ -shocks which have been used to provide solutions for Riemann problems in...

Retailer’s Optimal Ordering Policy for Deteriorating Inventory having Positive Lead Time under Pre-Payment Interim and Post-Payment Strategy

Management of inventory and its control for the retailers involves the procurement and storage of items for the smooth functioning of day-to-day business affairs. The procurement of goods depends on lead time and the payment mechanism. Thus, these components have a vital role in the optimal strategy for inventory control and management. As a result, these two components have a...

ABC Fractional Order Vaccination Model for Covid-19 with Self-Protective Measures

A mathematical model delineating the control strategies in transference of Covid-19 pandemic is examined through Atangana–Baleanu Caputo type fractional derivatives. The total count of people under observation is classified into Susceptible, Vaccinated, Infected and Protected groups (SVIP). The designed model studies the efficiency of vaccination and personal precautions...

Selection of Radial Basis Functions for the Accuracy of Meshfree Galerkin Method in Rotating Euler–Bernoulli Beam Problem

In this work, the radial basis function approximations are used to improve the accuracy of meshfree Galerkin method. The method is applied to the free vibration problems of non-rotating and rotating Euler–Bernoulli beams. The stiffness and mass matrices are derived by using conventional methods. In this meshfree method, only six nodes are considered within a single sub-domain...

Solving Fredholm Integral Equations Using Deep Learning

The aim of this paper is to provide a deep learning based method that can solve high-dimensional Fredholm integral equations. A deep residual neural network is constructed at a fixed number of collocation points selected randomly in the integration domain. The loss function of the deep residual neural network is defined as a linear least-square problem using the integral equation...

New Fractional Modelling, Analysis and Control of the Three Coupled Multiscale Non-Linear Buffering System

This study aims to investigate the complicated dynamical $$HCO_3^-/CO_2$$ buffering system using fractional operators which is not been investigated yet. We consider a new fractional mathematical model in the frame of fractional-order differential equations. In the proposed fractional-order model, we apply the Caputo-Fabrizio fractional operator with an exponential kernel. Then...

Analytical Study for Different Extremal State Solutions of an Irrigation Optimal Control Problem with Field Capacity Modes

In this paper we study the problem of daily irrigation of an agricultural crop using optimal control. The dynamics is a model based on field capacity modes, where the state, x, represents the water in the soil and the control variable, u, is the flow rate of water from irrigation. The variation of water in the soil depends on the field capacity of the soil, $$x_{FC}$$ , weather...

Analysis of deterministic models for dengue disease transmission dynamics with vaccination perspective in Johor, Malaysia

Dengue is a mosquito-borne disease which has continued to be a public health issue in Malaysia. This paper investigates the impact of singular use of vaccination and its combined effort with treatment and adulticide controls on the population dynamics of dengue in Johor, Malaysia. In a first step, a compartmental model capturing vaccination compartment with mass random...

Orthonormal Bernoulli Polynomials for Solving a Class of Two Dimensional Stochastic Volterra–Fredholm Integral Equations

Analyzing the mathematical models involving Itô integral, in particular in science and engineering has received much attention, and the reason for this issue is the randomness and lack of access to the exact answer of this type of models. For this purpose, in this paper, the approximate solution of two dimensional (2-D) stochastic Volterra–Fredholm integral equations (SVFIEs...