2023

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Analytical solutions of fractional partial differential equations for the second grade fluid flow.
(UMT Lahore, 2023) Maira Anwar
This thesis deals with unsteady flow of second grade fluid over an infinite plate. The governing equations for flow are developed through constitutive relations. Then classical model extended to fractional order model with power law fractional differential operator. The Laplace transform (LT) method, which is expressed in terms of series that meet the boundary conditions, is used to discover the analytical solutions. Some graphs are shown to illustrate the physical significance of flow parameters. Recent results from the existing literature are also recovered to validate.
Numerical modeling of SEIRV of re-infection rubella transmission and vaccination
(UMT Lahore, 2023) Samiullah
Rubella is an infectious illness that can spread anywhere in the world. In addition to the tropics, it also spreads in the subtropics. Although it is commonly known as a non-fatal condition, there are several circumstances in which it can be quite deadly. The development of the fetus is highly risky for pregnant women who have the Rubella virus. The purpose of this study is to look at a model of Rubella transmission while taking a vaccination drive into account as a measure of control. The endemic equilibrium and the disease-free equilibrium have been found using the SEIR-V mathematical model. The Jacobian matrix’s eigenvalues from the liberalization process create a threshold value for the spread of disease or the basic reproduction number. The selected value has been used to illustrate the situation when Ro is less than 1, demonstrating the existence and consistency of a disease-free equilibrium. A stable endemic equilibrium is discovered in the interim when Ro is greater than 1. Three numerical schemes, including Non Standard Finite Difference and Euler RK-4, are developed for the model’s numerical solution (NSFD). In this study, numerical simulations are employed to verify the conclusions of the analytical computations.
Computing fractional metric dimension of networks under operations
(UMT Lahore, 2023) Samreena Qaiser; M. Farhan Tahir; M. Mahib
Graph theory has received a lot of interest in recent years because of its many applications in domains including computational science, social networking sites, and communication networks. Graph theory has received a lot of interest in recent years because of its many applications in domains including information technology, networking platforms, and communication networks. The goal of this study is to look at local resolving sets in the complementing graph of sunflower networks. Sunflower networks, which are well-known graph topologies, are made up of a core vertex known as the sunflower center, which is linked to multiple unique petals. The complementary graph of the sunflower network, which is formed by swapping edges and non-edges, provides an interesting study field for analyzing graph features. Local resolving sets are vertices subsets that can independently determines the labels of every other vertices within a given distance. Let h=(j(h), k(h)) be a connected and finite graph. In this project, we are going to calculate the LFMD or the local fractional metric dimensions of the complement graphs of sunflower network via generating the classes ‘a’, ‘b’ and ‘ab’ class. We computed the generalized formulas for the LFMD of complementary sunflower network graphs. The entirety of the acquired results are demonstrated by the illustration of specific graphical representations pertaining to the under researched families of graphs.
A deep learning approach to analysis the Covid-19 disease spread in population
(UMT Lahore, 2023) Touseef Afzal
The susceptible, exposed, infected, hospitalized, recovered (SEIHR) model, a frequently employed framework for explaining the dynamics of the novel coronavirus (COVID-19), has been thoroughly examined, and I describe that study in my thesis. Our main interest is in the numerical solutions of this model, especially when using various step sizes with two well-known numerical methods, the RK-4 method and the Euler method. Our findings show a clear pattern in these numerical approaches’ behavior. Particularly, the Euler and Runge-Kutta Four Order (RK-4) approach both consistently produce accurate results when the step size is set to one, demonstrating their dependability in capturing the complex dynamics of the SEIHR model. Larger step sizes, though, provide a serious obstacle. Both the Euler and the RK-4 methods show this crucial shortcoming in such situations, failing to generate valid solutions and instead deviating from the desired results. In order to overcome this limitation, investigate a new approach that involves using a neural network technique to solve the SEIHR model. Our research yields a startling and encouraging finding: the neural network consistently produces precise solutions across a wide variety of step sizes. This exceptional robustness of the neural network method highlights its potential as a reliable substitute for solving the SEIHR model, especially when handling bigger step sizes. This study highlights the importance it is to using the right numerical techniques when working with intricate epidemiological models like the SEIHR model. Additionally, our study opens up a fruitful path for expanding our knowledge of the dynamics of the novel coronavirus and other infectious disorders. When bigger step sizes are required, the neural network approach proves to be an exceptionally useful tool. This finding has enormous potential for improving our capacity to forecast infectious disease behavior and, ultimately, to support public health decision-making and pandemic management.
Applications of bipolar soft sets on BCK-modules
(UMT Lahore, 2023) Madeeha Ilyas
The notion of BCK-module was established as an action of BCK-algebras on abelian groups. On the other hand bipolar soft sets have been developed to equip the notion of soft set with a polarity. In this thesis the notion of bipolar soft sets is applied on the notion of BCK-module and thereby the novel idea of bipolar soft BCK-module is introduced. In this regard, the fundamental operations on bipolar soft BCK-modules have been defined and discussed for various attributes. These operations included union, intersection, addition, complement and cartesian product of bipolar soft BCK-modules. Further, the notion of bipolar soft BCK-submodules is introduced and discussed for fundamental properties.
Impact of tangent hyperbolic fluid with nanoparticles attribution over a spinning body
(UMT Lahore, 2023) Nimra Shahzadi
In the forward stagnation-point zone of a sphere with an applied magnetic field, this work intends to investigate the nonlinear unsteady boundary layer flow and heat transfer of an incompressible tangent hyperbolic boundary layer flow. Bioconvection can improve the settling of nanoparticles, which is considered more realistic in this work. The Runge-Kutta fourth order technique calculates the converted conservation equations under physically boundary conditions. Previous research has validated the numerical code. The impact of numerous emerging non-dimensional parameters, such as the Weissenberg number (We), power law index (n), Prandtl number (Pr), Biot number (Bi), and dimensionless tangential coordinate (n), on velocity and temperature evolution in the boundary layer regime is explored in depth. Additionally, the impacts of these factors on temperature distribution and skin friction are studied. One of the most important discoveries of this study is that increasing the thermophoresis factor produces a decrease in the temperature profile at the surface. However, a further important finding of the current study is that the behavior of the species concentration decreases as Arrhenius activation energy increases. Fluid flow caused by a rotating body has been used in heat transformation systems for nuclear propulsion devices.
Development of spherical fuzzy hypersoft set with applications
(UMT Lahore, 2023) Naveed Qamar
In this dissertation, concept of spherical fuzzy hypersoft set is developed with application. The scope of this study may cover a wide range of applications in many fields of mathematical sciences. The proposed model bears the characteristics of most of the relevant existing models collectively and fulfills their inefficiencies by introducing a novel approximate approach. Spherical fuzzy hypersoft set (SFHSS) is an extension of traditional fuzzy sets that incorporate hypersoft sets and spherical functions. By incorporating hypersoft sets into SFHSS, one can handle situations where membership degrees are not precisely known or where gradual transitions between membership grades are required. SFHSS find applications in several domains where uncertainty and complexity are prevalent. Some examples include decision-making, pattern recognition, image processing, expert systems, data mining, and machine learning. The enhanced representational capabilities of SFHSS make them suitable for modeling and analyzing real-world problems. Overall, spherical fuzzy hypersoft sets provide a powerful framework for handling uncertainty, complexity, and imprecision in data modeling and analysis. They offer a more flexible and expressive representation of information, leading to improved decision-making and problem-solving capabilities in a wide range of applications.
Prevalance of tech neck syndrome and its association with chest expansion in university students
(UMT Lahore, 2023) Asad Baig; Ahmad Ilyas; Ali Hassan Bukhari; Usama Sarwar; Numan Arif; M. Mushtaq
Objectives: To find the prevalence of tech neck syndrome among university students who are on screen users and to find the significant association between tech neck syndrome and reduced chest expansion. Materials and methods: 100 confirmed cases of tech neck syndrome are taken who use on-screen devices on an average of about 4 or more than 4 hours and have significant forward head posture. Costovertebral angle was measured with the goniometer while the chest expansion was measured with the inches’ tape during respiration and inspiration phases, and the difference between them was recorded. Results: 54 participants out of 100 confirmed cases of tech neck syndrome have significantly reduced chest expansion, which is the final result of this study, while 46 participants have greater chest expansion and show that they are normal, but they have tech neck syndrome.
Analysis of Jeffrey fluid with generalized boundary conditions via Prabhakar fractional approach
(UMT Lahore, 2023) Syed Mohsin Raza Shirazi
This theoretical investigation aims to generalize the idea of fractionalized Jeffrey fluid flow present in this research work. Exact analysis of MHD natural convective flow of the Jeffrey fluid to derive analytical solutions with the non-integer order derivative Prabhakar fractional operator with non-singular type kernel along with application of generalized laws namely Ficks and Fouriers are reported here. This fractional operator has multi-parameter generalized Mittag-Leffler kernel. The fluid flow is elaborated near an infinitely vertical plate with characteristic velocity u0. The modeling of the considered problem is done in terms of the partial differential equations together with generalized boundary conditions. Appropriate sets of variables are introduced to transform the governing equations into dimensionless form. Laplace transform (LT) is operated on the fractional system of equations and results are presented in series form and also in the form of special functions. The pertinent parameters’ influence such as Pr, Gm, Sc, and Gr on the fluid flow is brought under consideration to reveal interesting results. In comparison, we noticed the Prabhakar-like non-integer approach shows better results than the existing operators in the literature, and graphs are drawn to show the results. Also, results are obtained in a limiting sense such as second grade fluid, Newtonian fluid in fractionalized form, as well as Jeffrey and viscous fluid models for classical form from Prabhakar-like non-integer Jeffrey fluid model.
Computing connection zagreb indices of molecular structures
(UMT Lahore, 2023) Alam Shair
CA topological index (TI) is a function that associates a numeric number to the under-studied molecular graph. Molecular descriptors play a fundamental role in the study of mathematical chemistry, especially quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR). In this thesis, we computed the first Zagreb index, second Zagreb index, modified first, modified second, modified third and modified fourth Zagreb indices, first multiplicative, second multiplicative, third multiplicative and fourth multiplicative Zagreb indices and modified first, modified second and modified third multiplicative Zagreb indices based on connection Zagreb indices of molecular structures such as carbon nanotubes.
Forward roll coating of a viscoplastic material onto a porous web
(UMT Lahore, 2023) Atika Farooq
In this thesis, when the web passes through a small gap between the two rigid rollers, a mathematical model of forward roll coating of a thin film of a viscoplastic material onto a moving porous web is studied. The law of conservation of mass and momentum in the light of lubrication theory are nondimensionalized and solutions for the velocity profile, flow rate, pressure distribution are calculated numerically by using Range-Kutta-Fehlberg’s method. It has been depicted that by altering (increasing/decreasing) the value of involved parameters, we can control the engineering quantities like velocity distribution, flow rate, pressure distribution, and penetration depth. Engineers working in the coating industries can utilize these results and can compare the results with the experimental data. Some results are shown graphically. It is found that the involved parameter is an element to control coating thickness, flow rate, and pressure-distribution.
Digital color image encryption generated by permutation layer and chen’s hyperchaotic system
(UMT Lahore, 2023) Qasim Ali
Data encryption and cryptography have many uses, including secure internet communications, medical informatics, security locks, multimedia systems, and secure information sharing (military forces), among others. A wall and a private encryption method are created by using chaotic or hyper-chaotic properties of the system, such as processing capacity, sensitivity, randomness, regularity, and a unique secret key. In this research, "Digital Color Image Encryption generated by Chen's hyper-chaotic system" is used to process digital image encryption, which adjusts color images to cipher images. This method demonstrates good and effective encryption and increases sensitivity in case of any cryptographic attack on the encrypted information.
Computation of local fractional metric dimension of certain families of graphs
(UMT Lahore, 2023) Ayesha Badar
Metric related graph parameters have been used as effective tools in various network domains where nodal distances are the focus of study. Some of these domains include computer networking, telecommunication and electrical networking. The fractional metric dimension is a recently developed variant of the metric dimension that is commonly used for non-integral linear programming problems. In this thesis, we will compute the local fractional metric dimension (LFMD) of certain circular ladders with pendent edges and convex polytopes. Further, the obtained results are illustrated with the help of examples.
Lanzhou index of graphs under the operations of product
(UMT Lahore, 2023) Sumbal
When working with chemical structures and molecular graphs, graph theory is in fact very important in the field of chemoinformatics. Topological indices (TIs), numerical parameters used in chemoinformatics for the study of these structures, are frequently used. A topological index is a mathematical formula that converts a molecular graph to a real number. If there are two graphs, S1 and S2, then TI(S1)=TI(S2). Various molecular features can be described and chemical behavior can be predicted with the aid of topological indices. The Wiener index, which was first presented by Harry Wiener in 1947, is one of the oldest and most well-known topological indices. We describe and study a novel topological index called the Lanzhou index, and we demonstrate that it outperforms a number of current indices on several benchmark datasets suggested by the International Academy of Mathematical Chemistry. We establish its extremal values and categorize its extremal graphs.
A theoretical approach towards interval-valued neutrosophic fuzzy soft set like structures with applications
(UMT Lahore, 2023) Kinza Kareem
This study analyses structures that are similar to interval-valued neutrosophic fuzzy soft set (IVNFSS), presenting a thorough theoretical foundation and demonstrating their practical application. This research demonstrates the inherent limits of soft sets, neutrosophic sets, and fuzzy sets, which led to the development of IVNFSS and IVNFHSS as a revolutionary method for dealing with imprecise and uncertain information. Soft sets, neutrosophic sets, and fuzzy sets have historically handled uncertainty. The theoretical framework is meticulously built, starting with a thorough literature analysis that highlights the shortcomings of current approaches and establishes the need for IVNFSS and IVNFHSS. The algebraic structures, mathematical operations, and features of IVNFSS and IVNFHSS are defined methodically, revealing the resilience and elegance of their underlying mathematics. The results of this study highlight the flexibility and effectiveness of IVNFSS and IVNFHSS. The research exhibits crucial theoretical features including union, intersection, complement, and De Morgan’s laws in the context of IVNFSS and IVNFHSS by thorough investigation. Furthermore, practical applications of IVNFSS and IVNFHSS are illuminated through illustrative examples and compelling case studies, providing tangible evidence of its effectiveness in domains like decision-making, pattern recognition, and expert systems. These findings highlight IVNFFSS’s tremendous potential as a useful tool for addressing real-world problems characterized by uncertainty and imprecision. The study advises a further investigation of IVNFSS and IVNFHSS across several domains, including artificial intelligence, data mining, and decision support systems, in light of these insightful findings. The research also urges the creation of software tools and algorithms to speed up the use of IVNFSS based techniques, enabling more effective and broad use. Academic and industrial cooperation is urged to make it easier to incorporate IVNFSS and IVNFHSS into real-world applications, thereby improving decision-making in both academic research and practical situations. In addition to providing a solid theoretical foundation for interval-valued neutrosophic fuzzy soft set-like structures, this paper also highlights how they have the potential to fundamentally alter how uncertainty is managed in a variety of applications and practitioners may open the way for more precise and robust decision-making processes by adopting IVNFSS-based methodologies, ushering in a new age of tackling complex, real-world situations rife with uncertainty and ambiguity.
Study on carbon nanotubes via connection number based Zagreb indices
(UMT Lahore, 2023) Ejaz ul Haq
Topological indices (TIs) are mathematical coding of the molecular graphs that predict the physicochemical, biological, toxicological and structural properties of the chemical compounds. To evaluate the physical and chemical properties of molecules, numerous TIs have been studied in the literature. A nanostructure belongs to a significant and an extensively investigated compound in chemical science. It has been derived through engineering mechanism at the molecular scale. Zagreb indices (ZIs) are the majority studied by TIs. TIs are classified on the basis of their degree, distance, and polynomial. Among these TIs, connection-based topological indices (ZCIs) have great significance. In this thesis, we compute several connection-based topological indices for carbon nanotubes graphs. We obtain first ZCI (1st ZCI) and second ZCI (2nd ZCI) and modified first ZCI (1*st ZCI), modified second ZCI (2*nd ZCI), modified third ZCI (3*rd ZCI) and modified fourth ZCI (4*th ZCI). Moreover, we compute multiplicative ZCI (MZCI), named as first MZCI (1st MZCI), second MZCI (2nd MZCI), third MZCI (3rd MZCI), fourth MZCI (4th MZCI) and modified first (1*st MZCI), modified second (2*nd MZCI), and third modified (3*rd MZCI) for carbon nanotubes graphs.
Development of an intelligent computing network for whooping cough like infection disease.
(UMT Lahore, 2023) Muhammad Khalil Tariq
In this thesis, the critical issues in global public health brought on by infectious diseases like whooping cough are discussed. Innovative methods for early diagnosis, monitoring, and control are required due to the rising occurrence of infectious diseases that are emerging and re-emerging. In order to do this, the author looked into the whooping cough epidemic using the SEIR model, a well-known mathematical framework in epidemiology. The study covered four different approaches to solving the SEIR model, each of which illuminated a different facet of disease transmission. The Euler approach was initially used by the author to attack the SEIR model, but as the inquiry went on, it became clear that this method had limits, especially with shifting step sizes. The author used the RK-4 method to overcome these difficulties, which improved the study and gave more precise insights into the dynamics of the disease. In addition, the Non-Standard Finite Difference (NSFD) approach was investigated, providing a nuanced viewpoint on the SEIR model. The author added artificial neural network (ANN) approaches to the research as a complement to the conventional mathematical techniques because they recognized the need for a comprehensive approach. This innovation was really helpful, especially when the earlier techniques had issues with certain step sizes. The author developed a more complete understanding of whooping cough transmission dynamics by combining ANN approaches with the SEIR model analysis. At the last, a neural network is applied for solving the SEIR model. After comparing the results of Euler, RK-4, NSFD, and Neural Network (NN), it was observed that NN is better than Euler, RK-4, and NSFD. The reason is that neural networks properly work at different step sizes, but Euler, RK-4, and NSFD are stuck at different step sizes. The neural network method stands out as the best option since it continuously produces estimates that are more accurate, no matter the circumstance. The work highlights the neural networks' capacity to provide more accurate results.
Artificial neural network-based numerical modeling of virus transmission in computer networks
(UMT Lahore, 2023) Haseeb Hussain Awaisi
In this thesis, artificial neural networks (NN) are used to predict virus transmission patterns in computer networks, introducing a new and data-driven strategy for improving network security. This is a difficult challenge because of how complicated the model is in real life. By training the neural networks (NN) on historical network data and virus transmission records, the model learns to recognize underlying patterns and factors that influence the spread of viruses in a network environment. By contrasting the efficiency of neural networks with traditional numerical techniques for resolving complex equations, this study explores a novel viewpoint. To illustrate the potential of the neural network-based technique in defining viral transmission via computer networks, specifically employ the Susceptible, Exposed, Infected, and Removed (SEIR) model. The neural network methodology is compared to widely used numerical methods like the Euler method and the Fourth Order Runge-Kutta method (RK-4) in this study on the dynamics of viral propagation through computer networks. The numerical methods, Euler and RK-4, are really good at staying stable and providing correct answers, but they run into issues with certain step sizes. Once the step size gets too big, both Euler and RK-4 stop working correctly. However, the neural network method works consistently for all step sizes. The importance of this study is seen in its comparison of the Euler and RK-4, and neural network approaches. The neural network method stands out as the best option since it continuously produces estimates that are more accurate, no matter the circumstance. The work highlights the capacity of neural networks to provide more accurate results, highlighting their promising role in boosting network security against emerging cyber threats, even though numerical approaches still serve their purpose well.
Numerical modeling
(UMT Lahore, 2023) Shaban
This thesis delves deeply into the intricate landscape of HIV/AIDS, providing a comprehensive overview spanning its precise definition, clinical manifestations, modes of transmission, diagnostic procedures, associated complications, and therapeutic interventions. Leveraging the potency of mathematical epidemiology, this research employs deterministic compartmental models, specifically a tailored SIR model, to analyze the complex dynamics governing the dissemination of HIV/AIDS. This tailored SIR model serves as the foundation for analyzing and modeling the distinctive attributes characterizing the transmission of the HIV/AIDS virus. A central theme of this research centers on the meticulous evaluation of various numerical techniques, including the Euler method, the RK-4 method, and the Non-Standard Finite Difference (NSFD) method, applied to HIV/AIDS epidemic models both with and without delay factors. These techniques are essential for understanding the intricacies of transmission dynamics in both scenarios. Consistently, the outcomes resoundingly favor the NSFD method for its unparalleled accuracy and efficacy, particularly when juxtaposed against conventional methodologies. In the realm of equilibrium points and reproductive numbers, the findings underscore the pivotal role played by the basic reproductive number R0 in ascertaining outbreak potential and devising containment strategies. Specifically, the study identifies distinct equilibriums — the disease-free and endemic equilibriums — and rigorously assesses their stability based on R0 values, offering invaluable insights into disease control and the potential for eradication. In summation, this thesis not only enriches our understanding of HIV/AIDS epidemiology but also bequeaths a robust mathematical toolkit for the meticulous assessment of its intricate dynamics. The insights garnered, particularly through the innovative NSFD method, hold profound promise for the formulation of optimal strategies in the relentless battle against this formidable disease.
Source/sink effect on MHD free convection flow of fractional Casson nanofluid under inclined magnetic field.
(UMT Lahore, 2023) Sania Sattar
The main purpose of this dissertation is to study the significance of fractional derivative for heat transport in drilling of nanofluid. The respective nanofluid formed by the suspension of clay nanoparticles in the base fluid namely Casson fluid. The physical flow phenomenon is demonstrated with the help of partial differential equations by utilizing the respective thermo-physical properties of nanoparticles. The geometric and thermal conditions are imposed in flow domain. The governing equations with respect to time replaced by the new hybrid fractional derivative namely, constant proportional Caputo (CPC) and then solved analytically for temperature and velocity fields with the help of Laplace transform. The transformed solutions for energy and momentum balances are appeared in terms of the series form. Further, the influence of flow parameters and fractional parameters  and  on the temperature and velocity fields are graphically underlined and discussed using mathematical software MATHCAD.

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