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A NOVEL STUDY OF DISTANCE BASED SIMILARITY MEASURES ON GLIVIFSESs Similarity plays an essential rule in pattern recognitions, in image processing and interdisciplinary fields such as statistics, information retrieval and data science. “Generalized linguistic interval valued intuitionistic fuzzy soft expert sets” (GLIVIFSESs) is comprehensive model in fuzzy algebra which allows flexi and more hesitant information in the form of intervals with expert expertise. We developed different types of similarity measures on GLIVIFSESs. Also separately for each similarity measure we constructed practical problems from real world data examples and checked-out the accuracy level of these measures. Behind similarity measures we attempted to apply dissimilarity measure, which plays an essential role in decision making problems. In which we firstly introduced the mathematical expression to measure dissimilarity for GLIVIFSESs and then tested the validity of that dissimilarity measure by considering the practical example related to judgments regarding the authorities of “X” state education department, and we obtained mostly accurate result. After that we used the idea of Entropy and employed it in similarity measurements which provided us comparatively most accurate results. We also introduced the concept of linguistic fuzzy implication for distance measure between GLIVIFSESs and then employed the exports opinions under linguistic fuzzy implication environment and obtained considerable accurate results.
Development of Derivative Free Iterative Methods With Memory for Nonlinear System In this research, three new three-step derivative-free methods are developed for solving system of nonlinear equations. Two of them are memory methods of convergence order 8.36 and 10, and the third method without memory is of convergence order 8. An inverse first-order divided di¤erence operator for multivariable functions is applied to prove the local convergence orders of these methods. Numerical results are provided to support the theoretical conclusions. The comparison with some known methods in the literature shows that the proposed methods are numerically efficient as compared to these methods.
Swirling Flow of Maxwell Fluid with Bioconvection Phenomenon Dynamics of non-linear fluid viscoelastic fluid with bioconvective properties is the core concern of the present thesis. There are many applications for non-linear fluids can be found in industry. Such as production of polymer and plastic sheets etc. encounter these types of the fluid flow. Therefore, in this era the scientists put their efforts to investigates the flow and thermal transport features of non-Newtonian fluids. These types of the liquids include time-dependent, timeindependent and viscoelastic type fluids. The viscoelastic type of fluid exhibits both viscous and elastics effects. The deformations tensor for viscoelastic non-linear fluids is used in empirical model called “Maxwell fluid model”. This model is the part of the present study in swirling type flow phenomena which is induced by rotating cylinder. Both Dufour and Soret effects are also included in the energy equation for the thermal analysis. The governing equations are changed into a set of nonlinear ordinary differential equations with appropriate flow ansatz. In MATLAB bvp4c, the converted nonlinear ordinary differential boundary value problem is solved with suitable boundary conditions. The impacts of dimensionless factors on velocity, temperature, concentration, and concentration of microorganisms are visually depicted in graphical abstract using a comparison of constant wall temperature (CWT) and prescribed surface temperature (PST).
CONSTRUCTION OF HIGHER ORDER TECHNIQUES FOR MULTIPLE ROOTS OF NONLINEAR EQUATIONS In this dissertation, higher order methods have been studied for finding multiple roots of single variable non-linear equation. We have developed here third, sixth and seventh order iterative methods for finding multiple roots of non-linear equation that may arise in modelling of real world with non-linear phenomena. These multiple root finding methods are based on the method developed by Thota and Shanmugasundaram [1] for determining simple roots. It is observed that newly developed methods have good comparison with method of same order. Their efficiency performance is tested on a number of relevant numerical problems.
Investigation of coefficient inequalities for certain New subclasses of analytic functions The aim of this research is to define and discuss some new subclasses of starlike and convex functions in an open unit disk. The q-theory and q differential operators will be used to present the q-version of already existing results on starlike and convex functions. The classes of analytic functions with respect to the symmetric point will be explained with the help of q-derivative certain new classes of q-starlike and q-convex functions with respect to symmetric points subordinated with exponential functions will be introduced, and these classes will further be modified by using exponential function with subordination technique. Coefficient inequalities for the functions belonging to the new classes will be investigated. We will determine the possible upper bound of the 3rd Hankel determinant for the q-starlike and q-convex functions. The relevant connections of our new classes and results to known ones will be also pointed out.
Impact of Magnetic Field on Hybrid Nanofluid Flow in the Presence of Convective Boundary Conditions This study aims to examine how the presence of an electrically conducting hybrid nanofluid affects the flow when the fluid is flowing over a porous surface. The study also takes into consideration the convective boundary conditions. The governing equations for the conservation of mass, momentum and energy for the hybrid nanofluid flow over the exponentially stretching surface are introduced. By employing the similarity transformation approach, the set of partial differential equations are transformed into a set of non-dimensional ordinary differential equations. The bvp4c method is utilized to solve these governing equations in order to obtain velocity and temperature profiles. The results indicate that solutions exist for cases involving the assisting and opposing flows. The study presents the findings of a boundary layer analysis considering different volume fractions of composite nanoparticles, suction/injection parameter, magnetic parameter, Eckert number and Biot number. The outcomes demonstrate that the presence of nanoparticles has a notable influence on drag force and Nusselt number within the boundary layer. Additionally, the study establishes the relationship between the variations in surface skin friction and heat transfer for both assisting and opposing flow scenarios.
Modification of Finite Difference Scheme for Time-fractional Hyperbolic Problem with Stability Analysis In this thesis the modification of finite difference scheme for the time-fractional wave problem with stability analysis for one- and two-dimensional time fractional wave equations (1D-TFWE and 2D-TFWE, respectively) on a finite domain is investigated. In the empire of mathematical physics and engineering, it has been recently discovered that the majority of physical processes give fractional order wave equations when modelled. To examine the techniques for solving fractional order wave equations and turn this scenario into an attractive research project, the precise solutions are crucial. Furthermore, problems in physics, environmental science, biology, and other fields of application have been modeled using fractional wave equations. For the (1D-TFWE) and (2D-TFWE), a Crank-Nicolson difference approximation is proposed. We explored the method's stability and convergence using mathematical induction. Finally, some numerical examples are shown. The numerical result and our theoretical analysis accord quite well.
A NEW HOMOTOPY TECHNIQUE FOR SOLVING SYSTEM OF NONLINEAR EQUATIONS In this study, Örst of all two new optimal fourth order iterative techniques have studied for solving single variable non-linear equations. These techniques need evaluation of one Örst derivative and two function evaluation that satisfy the Kung-Traub conjecture. These numerical techniques are then extended to techniques for solving system of non-linear equations. The establishment and execution of these techniques for solving system of nonlinear equations is based on the concept of element wise vector multiplication and diagonal matrix. In case, Jacobian matrix becomes singular at any stage because of approximation, the above techniques would fail. In order to overcome this di¢ culty, homotopy techniques for solving system of non linear equations were introduced. Theoretical convergence of modiÖed iterative techniques are proved through analysis theorems and numerical convergence through real time applications are provided to test the performance of these techniques.
q-Extension of Starlike functions with respect to symmetric points subordinated with q-sine function This thesis aims to introduce and characterize novel subclasses of univalent functions within the open unit disk. The utilization of q-calculus will be employed to establish the q-extension of starlike and convex functions related to symmetric points. Additionally, we will investigate notable properties, including bounds on the coefficients of analytic functions, the Zalcman functional, and the Fekete–Szego inequality. Furthermore, we will explore upper bounds on ˝Hankel Determinants for functions belonging to these newly defined classes. It will be shown that newly obtained results are advanced as compare to the already derived results by numerous researchers in the field of Geometric Function Theory. The special cases of newly derived results will be presented in the form of corollaries.
ANALYSIS OF STAGNATION POINT FLOW OF NANOFLUID OVER A STRETCHING SURFACE Nanofluids are heat transmission liquids with better thermo physical features and heat transfer capabilities that can improve the performance of several kinds of devices. Nanotechnology is significant in numerous categories, including heat transfer practices and energy applications. The present study examines the flow of Prandtl-Eyring nanofluid flowing over a stretching sheet placed in a porous medium. The fluid flow is developed in the presence of stagnation point and an inclined magnetic field. The heat and mass transfer characteristics in the flow regime are monitored using the Buon-giorno nano-model. The fluid model is presented in the form of partial differential equations and in order to convert these partial differential equations into ordinary differential equations, similarity transformations are utilized. Bvp4c method, a numerical technique is employed to solve the nonlinear ordinary differential equations. The effects of significant parameters on velocity, temperature and concentration profiles are illustrated graphically. The skin friction coefficient, Nusselt number and Sherwood number for the flow are calculated and examined numerically. The skin friction enhances for large values of magnetic and suction parameters and the opposite trend is encountered for the Nusselt and Sherwood numbers.
Impact of Inclined Magnetic Field on Peristaltic Flow of Ellis Fluid in a Curved Channel The primary goal of this thesis is to investigate the impact of inclined magnetic field and partial slip on the peristaltic flow of Ellis fluid. A mathematical formulation of the problem for the peristaltic flow of MHD Ellis fluid has been created. Furthermore, the walls of the channel are considered to be curved. The perturbation technique is used to address the problem that has been simulated. The challenge is made simpler by employing the low Reynolds numbers and long wavelength approach. The effects of diverse parameter on streamlines, longitudinal velocity, and pressure are investigated. The graphs for longitudinal velocity, stream function, pressure gradient are achieved using Mathematica software.
ANALYSIS OF WALL PROPERTIES AND SLIP PARAMETER ON THE PHAN-THIEN-TANNER (PTT) FLUID This thesis delves into a comprehensive exploration of the peristaltic movement of a nonNewtonian Phan-Thien-Tanner (PTT) fluid within a symmetric flexible channel characterized by sinusoidal peristaltic waves. The study employs the long wavelength and low Reynolds number approximation, focusing on the flow within a wave frame of reference that travels at the velocity of the peristaltic waves. The investigation encompasses a detailed analysis of the influences of wall properties, porosity, and slip parameter on the behavior of the PTT fluid. The mathematical representation of the system relies on partial differential equations (PDEs), with subsequent utilization of similarity transformations to effectively reduce the number of dependent variables. The analytical solution is employed to resolve mathematical complexities and provide conclusive results for the problem. Through the presentation of graphs, the study meticulously examines the impact of various physical parameters on streamlines, pressure distribution, and velocity within the system.
A Novel Study of Q-Rung Orthopair Interval Valued Fuzzy Soft Expert Sets The research introduces Q-Rung Orthopair Interval Valued Fuzzy Soft Expert Sets, which serve as a robust tool for decision-making. By integrating Interval-Valued Intuitionistic Fuzzy Soft Expert Sets and Q-Rung Orthopair Fuzzy Sets, this approach effectively handles multiple-criteria decision-making problems. The primary objectives of this study involve creating a mathematical framework, introducing new aggregation operators and improving the overall decision-making process. To achieve these goals, the research explores the structure of Q-Rung Orthopair Interval Valued Fuzzy Soft Expert Sets and the integration of aggregation operators. The methodology encompasses the development of a theoretical framework, the Definition of algorithms and the evaluation of their performance. Ultimately, this study contributes to enhancing decision-making efficiency and broadening the application of thesetechniques across various domains.
NUMERICAL STUDY AND STABILITY ANALYSIS OF PARABOLIC EQUATION OF FRACTIONAL ORDER Nowadays the research community prefers fractional calculus over classical calculus, as fractional calculus (FC) has extensively explored the physical properties of fractional-order differentials and integrals. The main reason behind this is that classical calculus deals with more specific behavior, whereas fractional calculus deals with more generic behavior. In this framework, this thesis witnesses the numerical study of the fractional-order parabolic equations. In the modeled problem the fractional-order derivative is assumed in the Caputo sense due to its numerous advantages—the modeled time-fractional parabolic problem is discretized using the Crank-Nicolson method. The thesis also provides a comprehensive study of stability and convergence analysis of the proposed mathematical method. To demonstrate the accuracy as well as efficiency of the scheme, numerical problems with various fractional order derivatives are finally given and compared with the exact solutions. Furthermore, a comparative numerical study is done to demonstrate the efficiency of the proposed method. The thesis is finally summarised in the conclusion.