Contents
Multivariate Fuzzy-Random and Stochastic Arctangent, Algebraic, Gudermannian and Generalized Symmetric Activation Functions Induced Neural Network Approximations
1 Fuzzy-Random Functions and Stochastic Processes Background
2 About Neural Networks Background
2.1 About the Arctangent Activation Function
2.2 About the Algebraic Activation Function
2.3 About the Gudermannian Activation Function
2.4 About the Generalized Symmetrical Activation Function
3 Main Results
References
From Koeller's Idea to Modern Fractional Calculus: Fractional Polynomial Operators
1 Introduction
1.1 The Koeller Main Idea and Its Background
1.2 The Koeller's Polynomial Operators
1.3 Koeller Example of a Polynomial Operator
1.4 Outcomes of the Koeller's Approach and Beyond
2 Fractional Calculus in Viscoelasticity
2.1 Stress-Strain Viscoelasticity Response and Hereditary Integral Construction
2.2 Discrete Spectra as Sums of Exponents
2.3 Viscoelastic Polynomial Fractional Model in Terms of Atangana-Baleanu Derivative
3 Some Comments on the Bagley-Torvik Equation
3.1 The Initial Formulation and Assumed Approximations
3.2 Bagley-Torvik Equation in Terms of Polynomial Caputo-Fabrizio Operators
4 Polynomial-Based Relationships Between Fractional Operators with Various Kernels
4.1 Riemann-Liouville and Caputo Formulations as Fractional Caputo-Fabrizio Polynomials
4.2 Fractional Operator with a Mittag-Leffler Kernel and Fractional Caputo-Fabrizio Polynomials
5 Final Remarks
References
On Weighted Fractional Operators with Applications to Mathematical Models Arising in Physics
1 Introduction
2 Weighted Generalized Hilfer-Prabhakar Fractional Derivative and Weighted Laplace Transform
3 Free-Electron Laser Equation Involving Weighted Generalized Fractional Operators
4 Fractional Kinetic Equation Involving Weighted Generalized Fractional Operators
5 Conclusions
References
Numerical Solution of Eighth Order Boundary Value Problems by Using Vieta-Lucas Polynomials
1 Introduction
2 Preliminaries
2.1 Shifted Vieta-Lucas Polynomials and Its Operational Matrix of Differentiation
3 Mathematical Model and Numerical Scheme
4 Convergence and Error Analysis
5 Numerical Examples
6 Results and Discussions
7 Conclusion
References
The Mexican Hat Wavelet Transform on Generalized Quotients and Its Applications
1 Introduction
1.1 Generalized Quotients
2 The Mexican Hat Wavelet Transform (MHWT) on the Space H
3 Operational Properties
4 The Exchange Property
5 Conclusions
References
Second-Order Nonlinearity of a Boolean Function Class with Low Spectra
1 Introduction
2 Preliminaries
3 Main Result
4 Conclusion
References
On Semimonotone Z-Matrices
1 Introduction
2 Preliminaries
3 Main Results
4 Results for Matrices with Specific Sign Patterns
5 Conclusions
References
Mathematical Analysis of Hall Effect and Hematocrit Dependent Viscosity on Au/GO-Blood Hybrid Nanofluid Flow Through a Stenosed Catheterized Artery with Thrombosis
1 Introduction
2 Mathematical Formulation
2.1 Governing Equations
2.2 Non-dimensionalization of Governing Equations
3 Solution Process
4 Result and Discussion
4.1 Velocity Profile
4.2 Flow Rate, Wall Shear Stress and Impedance
4.3 Velocity Contour
5 Conclusion
References
A Computational Investigation of the Characteristics of Velocity Slips and Convective Boundary Conditions in Maxwell Nanofluid Flow over a Permeable Stretching Surface with Activation Energy
1 Introduction
2 Mathematical Modelling
3 Local Skin-Friction Coefficients, Nusselt Number and Sherwood Number
4 Implementation of Numerical Technique
4.1 Solution Procedure
4.2 Results Validation
5 Results and Discussion
6 Conclusions
References
Modelling Pulsatile Blood Flow Using Casson Fluid Model Through an Overlapping Stenotic Artery with Au-Cu Hybrid Nanoparticles: Varying Viscosity Approach
1 Introduction
2 Mathematical Formulation
2.1 Governing Equations
2.2 Non-dimensionalization
2.3 Radial Coordinate Transformation
3 Solution Process
3.1 Discretization
4 Results and Graphical Analysis
5 Conclusions
References
Generalized Solitary Wave Approximate Analytical and Numerical Solutions for Generalized Damped Forced KdV and Generalized Damped Forced MKdV Equations
1 Introduction
2 Approximate Analytical Solutions of GKdV and GMKdV Equations
3 Bifurcation Analysis of GKdV Equation and GMKdV Equation
4 Approximate Analytical Solutions of GDFKDV and GMDFKDV Equations
5 Generalized Solutions of GDFKDV and GMDFKDV Equations
6 Analysis of GKdV and GMKdV Equation with the Help of Pseudo-spectral Method
7 Conclusions and Future Work
References
NIPG Method on Shishkin Mesh for Singularly Perturbed Convection-Diffusion Problem with Discontinuous Convection Coefficient
1 Introduction
2 Stability and Solution Decomposition
3 Piecewise Equidistant Mesh and NIPG Method
3.1 Shishkin Mesh
3.2 The NIPG Method: Procedure and Properties
4 Error Estimations: Sharp Bound on Shishkin Mesh
4.1 Interpolation Error
5 Uniform Convergence
6 Numerical Result and Implementation
7 Conclusion
8 Discussion
References
Simultaneous Action of Modulated Temperature and Third Diffusing Component on Natural Convection
1 Introduction
2 Governing Equations
3 Basic State
4 Perturbation
5 Non Dimensionalised Parameter
6 Weakly Non-linear Stability Analysis
6.1 Expansion of Variables
6.2 First-Order Solution
6.3 Second-Order Solution
6.4 Third-Order Solution
7 Results and Discussion
8 Conclusion
References
Approximate Numerical Solution of the Nonlinear Klein-Gordon Equation with Caputo-Fabrizio Fractional Operator
1 Introduction
2 Basic Tools
3 General Description of FHPTM Using CF Operator
4 Applications
5 Conclusion
References
On a Class of New q-Hypergeometric Expansions as Discrete Analogues of the Erdélyi Type q-Integrals
1 Introduction
2 Motivation and Objective
3 Discrete Extensions of Erdélyi Type q-Integrals or New q-Hypergeometric Expansions
4 Proof of q-Hypergeometric Expansion (3.1) Corresponding to Erdélyi Type Integrals with t - 1 as One of the Numerator Parameters
5 Proof of the New q-hypergeometric Expansion (3.2) Corresponding to Erdélyi Type Integrals Without t - 1 as One of the Numerator Parameters
6 Conclusion
References
Mathematical Modelling of an Incompressible, Newtonian Blood Flow for the Carotid Artery
1 Introduction
2 Material and Methods
2.1 Elastic Model
2.2 Spatial Discretization
2.3 Boundary Conditions for the Tangential Velocity
2.4 Solve for the Pressure
3 Result and Discussions
4 Conclusion
References
The Effect of Peripheral Layer Thickness on Pulsatile Flow of Blood in Human Femoral Artery
1 Introduction
2 Mathematical Formulation and Solution
3 Significance of Hemodynamic Near Wall Parameters
3.1 Wall Shear Stress
3.2 Oscillatory Shear Index
4 Result
5 Discussion
6 Conclusion
References
A Computational Study of Local Fractional Helmholtz and Coupled Helmholtz Equations in Fractal Media
1 Introduction
2 Mathematical Fundamentals
3 Analysis of LFSDM
4 Application of LFSDM
5 Numerical Results and Discussion
6 Conclusions
References
Estimation of Software Reliability Using Lindley Distribution Based on MLE and UMVUE
1 Introduction
2 Methods to Estimate Reliability
2.1 Maximum Likelihood Estimation Method
2.2 Uniform Minimum Variance Unbiased Estimator Method (UMVUE)
3 Reliability Estimations of Lindley Distribution Model
3.1 MLE of R(t)
3.2 UMVUE of R(t)
4 Datasets
4.1 Data Set I
4.2 Data Set II
4.3 Data Set III
4.4 Data Set IV
4.5 Data Set V
4.6 Data Set VI
5 Conclusion
References
Solution of Fractional Order Foam Drainage Equation Using Shehu Transform
1 Introduction
2 The Model
3 Preliminaries
3.1 Some Important Definitions of Fractional Order Derivative
3.2 Shehu Transform
3.3 The Combined Shehu Accelerated Adomian Decomposition Method
4 Results and Discussion
5 Conclusion
References
On a Class of Macrobert's Type Finite Integrals Involving Generalized Hypergeometric Functions
1 Overview
2 Eulerian's Type Integrals
References
Irreversibility Analysis in Micropolar Thermofluidics Involving Deforming Sheet
1 Introduction
2 Mathematical Formulation of the Problem
3 The Transformation
4 Quantities of Interest
5 Numerical Solution Methodology
6 Entropy Generation Analysis
7 Results and Discussion
8 Conclusion
Appendix
References
A Variational Description to Modulational Instability Criterion
1 Introduction
2 Criterion of Modulational Instability (MI)
3 Implement of Method for Solving the Model Equation
4 Graphical Sketch
5 Result and Discussion
References
Applications of General Summation Formulas Contiguous to q-Kummer Theorems
1 Introduction and Motivation
2 Main Results
3 Applications
4 Summations of q-Lauricella Functions
5 q-Laplace Transform
6 Conclusion
References
MHD Radiative Casson Fluid Flow over a Non-linear Extending Surface with Cross-Diffusion Impact in the Presence of Buoyancy and Porous Impacts
1 Introduction
2 Problem Structure
3 Results and Discussion
4 Conclusion
References
A Comparative Analysis of Different Basis Functions for Constructing BĂ©zier Curves
1 Introduction
2 Theoretical Foundation
2.1 BĂ©zier Curves
2.2 Cubic Trigonometric BĂ©zier Curves
2.3 Properties of T-BĂ©zier Curves
3 Composition of T-BĂ©zier Curves
3.1 Parametric Continuity Constraints of T-BĂ©zier Curves
3.2 GT-BĂ©zier Curves
3.3 GBT-BĂ©zier Curves
3.4 Properties
4 Comparative Analysis
4.1 Cubic BĂ©zier Curves vs Cubic Trigonometric BĂ©zier Curves
4.2 Cubic BĂ©zier Curves vs Other Basis Functions
5 Conclusion
References
Study of Copper-Water Nanofluid Flow over an Isothermal Moving Sheet
1 Introduction
2 Mathematical Analysis
3 Comparability Variables
4 Manifesto of Investigation
5 Validation of Solution Methodology
6 Results Analysis
7 Conclusions
References
Thermal Instability of Rivlin-Ericksen Elastico-Viscous Nanofluid Saturated by a Porous Medium with Rotation
1 Introduction
2 Governing Equations
2.1 Basic Solution
2.2 Linear Analysis
3 Normal Mode Method
3.1 Stationary Mode of Convection
3.2 Non-linear
4 Heat/Nanoparticle Concentration Transport
5 Results/Discussion
5.1 Linear Stability Analysis
5.2 Non-linear Stability Analysis
6 Conclusions
References
Study of the Convective-Radiative Moving Porous Fin with Temperature-Dependent Variables
1 Introduction
2 Problem Description
2.1 Particular Cases
3 Computational Methods
3.1 Legendre Wavelet Collocation Method
3.2 Least Square Method
3.3 Moment Method
4 Exact Solution
5 Results and Discussion
6 Conclusion
References
Multi-objective Linear Fractional Transportation Problem Under Uncertainty
1 Introduction
2 Mathematical Model
3 Definitions
4 Solution Methodology
4.1 Stepwise Algorithm for Fuzzy Programming Problem
4.2 Weighted Sum Method (WSM) and Stepwise Solution
4.3 Global Criterion Method (GSM) and Stepwise Solution
5 Numerical Illustration
6 Results
7 Conclusion
References
Mathematical Model on the Effects of Environmental Pollution on Biological Populations
1 Introduction and Preliminaries
2 Mathematical Model
3 Result in Terms of Incomplete -Functions
4 Special Cases
5 Conclusion
References
High Gain Calculation & Simulation for Antenna Design for 6G Wireless Applications
1 Introduction
2 Antenna Geometry and Design
3 Conclusion
References
Non-similarity Solutions of MHD Boundary Layer Flow
1 Introduction
2 Governing Equations
3 Görtler Transformation
4 Numerical Solution
5 Results and Discussions
6 Conclusions
References
Deferred (vm, f)-Statistical Convergence of Order in Normed Space
1 Introduction
1.1 Introduced Definitions
1.2 Particular Cases
2 Main Results
2.1 Inclusion Relations on DS(vm,f,X) and D(vm,f,X)
2.2 Relationship Between DS(vm,f,X) and D(vm,f,X)
3 Comparison of Inclusion Relations Between Two Deferred Sequences
References
Integral Formulae Associated with the S-Function, H -Function and the Aleph Function
1 Introduction
2 Fractional Integrals
3 The Fractional Integral Formulae
4 Special Cases of Theorem 1
5 Special Cases of Theorem 2
6 Special Cases of the Fractional Integral Formulae
7 Conclusions
References
Air Quality Index: A Comparative Study of Air Quality in Jaipur When the Pre-lockdown and Post-lockdown Phases Are in Effect
1 Introduction
2 Research Methodology
2.1 Study Area
2.2 Air Quality Index
3 Result and Discussion
3.1 Particulates, Fine (PM2.5)
3.2 Coarse Particulate Matter (PM10)
3.3 Major Pollutant
4 How to Control Air Pollution?
4.1 Control Measures to be Taken by the Government
4.2 Control Measures to be Taken by the General Public
5 Conclusions
References
Mathematical Study on Corona-Virus (COVID-19) Disease Transmission and Its Stability Through SEIR Epidemic Model
1 Introduction
2 Model Formulation
3 Model Analysis
3.1 Equilibrium Points: Existence and Stability
4 Model Validation and Parameter Estimation
5 Conclusion
References
Author Index