2022

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A generalization of nadler fixed point result in hausdorff double controlled metric type space
(UMT Lahore, 1-8-2022) Muhammad Tariq
In 2020, Nayab Alamgir [9] showed that every controlled metric type space (; q) induces a Hausdorff controlled metric type space on the class of closed subsets of which is also complete if (; q) is complete. He also defined multivalued almost F-contractions on Hausdorff controlled metric type spaces and proved some fixed point results. In this thesis, we will show that every double controlled metric type space makes a Hausdorff double controlled metric type space (H; CD()) where CD() is the collection of all non-empty closed subsets of and if (; q) is complete then (H; CD()) is also complete. We will also demonstrate multivalued almost F-contractions on Hausdorff double controlled metric type space and we will derive a few fixed point results.
A real-life MCDM problem of selecting a university in the UK for post-graduate studies
(UMT Lahore, 2022-10-29) Zulaikha Aftab Sheikh
Education is the finest investment one can make as it serves as a cornerstone for a better future. Higher education offers opportunities for individuals to thrive and compete with the challenges of the modern era. Highly educated individuals with diverse experience are more likely to achieve high-paying jobs. Every student who is pursuing higher education wants his degree to be affiliated with some well-established institute. One can only gain a successful career if he has some remarkable research included in his resume. Mathematical science is particularly one of the most complex and advanced degrees. Most students, especially from third-world countries, choose the United Kingdom to pursue their post-graduate (master’s and doctoral) degrees. The reason behind this, most countries are way behind in the latest research and up-to-date applications of mathematical sciences, while the United Kingdom has a well-regarded center of advanced research institutions. Lack of educational infrastructure, research centers, and funding are the most common issues that urge students to abandon their own country in pursuit of a better future. Therefore, selecting a university in the UK is a big challenge for students. To overcome this challenge, mathematical modeling for selecting a university is performed to solve this real-life problem, resulting in a multi-criteria-decision-making (MCDM) problem. Data for this problem has been arranged from the university’s websites. In this study, MCDM techniques are used to assess the standards taken into account while selecting a university. Two popular MCDM techniques are used: Analytical Hierarchy Process (AHP) is used to calculate the weights for each qualitative and quantitative criterion, and another technique namely VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) is used to rank the alternatives of problem. The outcomes are very promising, programming code for the AHP and fuzzy VIKOR algorithms is also implemented in order to broaden the work application to time series analysis and the creation of algorithms for graph theory, machine learning, pattern recognition, and artificial intelligence.
A study on modeling and designing an MCDM model of contact lens selection
(UMT Lahore, 2022) Umama Shahzadi
Owing to the current technical and societal changes, many factors play a significant role in the selection of a suitable contact lens, making a decision more complex. In recent years, the issue of selecting an eye lens has gained greater attention. Lenses are widely used around the world, and they are especially popular among young people. However, little is known about the aptitude and inclination of youngsters in various parts of the world, such as Pakistan. As a result, information is needed to be provided to individuals with regard to the purchase of lenses. Mathematical modelling of the lens selection problem is performed to deeply analyze this real problem, resulting in the multi-criteria decision-making (MCDM) scenario. Therefore, data has been collected through the survey and a bunch of websites of different brands available in Pakistan. An ample amount of study and research has been done to make a decision matrix that gives valuable insight into the collected data. In this study, multi-criteria decision-making techniques, i.e., fuzzy TOPSIS and fuzzy VIKOR, are used to analyze alternatives and assess the standards taken into account while choosing the lenses. Operational research encompasses MCDM, whose main objective is evaluating, ranking, and choosing among options for numerous and competitive criteria. Programming is used to evaluate results and to find the most suitable lens brand considering a particular scenario. The comparative analysis is conducted to compare the outcomes of the two MCDM methods.
A study on quantum and post quantum integral inequalities
(UMT Lahore, 2022-07) Muhammad Abbas
In this thesis work, we use quantum integrals to derive Hermite-Hadamard inequalities for preinvex functions and demonstrate their validity with mathematical examples. We use the k-2 -quantum integral to show midpoint and trapezoidal inequalities for k-2 -differentiable preinvex functions. Furthermore, we demonstrate with an example that the previously proved Hermite-Hadamard-type inequality for preinvex functions via k-1 -quantum integral is not valid for preinvex functions, and we present its proper form. We use k-1 -quantum integrals to show midpoint inequalities for k-1 -differentiable preinvex functions. It is also demonstrated that by considering the limit k -> 1 and φ(α2; α1) = φ(α1; α2) = α2 - α1 in the newly derived results, the newly proved findings can be turned into certain known results.
A theoretical development of cubic pythagorean fuzzy soft set.
(UMT Lahore, 2022-02) Rimsha Shafaqat
Pranjal and Palash (2019) introduced cubic pythagorean fuzzy sets, that incorporates both interval-valued pythagorean fuzzy sets (IVPFS) and pythagorean fuzzy sets (PFS) at the same time, allowing for a more targeted approach to deal with uncertainty. It is challenging to utilise traditional approaches to handle complex issues like economics, engineering, or the environment because of the complexities in those fields. In order to get a better solution cubic pythagorean fuzzy soft set (CP F Ss) introduces, which is the hybrid of interval-valued pythagorean fuzzy soft set (IVPFSs) and pythagorean fuzzy soft set (PFSs). Cubic pythagorean fuzzy soft set (CP F Ss) is more efficient than cubic intuitionistic fuzzy soft set (CIFSs). It drives you to improve the capability of (CIFSs) in difficult decision making since it represents the ambiguity or ill-defined information. In this study, we defined various internals and externals of CP F Ss, set operators, aggregation operators and applications of distance measures for (CP F Ss) which are shown in disease diagnosis decision-making problems.
AHP method for the optimal hotel selection in China by online data
(UMT Lahore, 2022) Mubashra Hassan
Luxury hotel guests' expectations and opinions of the service and amenities are mostly responsible for their satisfaction or dissatisfaction (Lu, Berchoux, Marek & Brendan, 2015). In luxury hotels, customers are increasingly looking for high-quality services and high-value goods (Walls, Okumus, Wang & Kwun, 2011). Also, based on guest reviews, TripAdvisor offers extensive information on what luxury hotels do well and incorrectly (O'Connor, 2010). Social choice is a theoretical framework for analyzing the process of combining individual opinions, preferences, interests, or welfare in order to arrive at a collective decision or, in some cases, social welfare. The basic goal of this thesis is to aggregate the overall rating based on online ratings from guests by managing a social choice analysis of online hotel ratings. Multi-Criteria Decision Making (MCDM) is the application of computational methods that incorporate several criteria and order of preference in evaluating and selecting the best option among many alternatives based on the desired outcome. Also, the AHP provides a rational framework for a required decision by quantifying its criteria and alternative options and linking those elements to the overall goal. Finally, online ratings exert strong effects on hotel choice at the 5-star rating level. An experiential study is being conducted using real Trip.com data to demonstrate the applicability and superiority of our problem allegation.
Applications of non-integer differential operators in transport phenomena
(UMT Lahore, 2022-10-14) Hafiz Aziz Ur Rehman
The aim of this dissertation is to analyze the heat and mass transference of non-Newtonian fluids over a vertical plate with different set of thermal boundary condition such as ramped conditions, Newtonian heating, exponential heating and variable temperature under the considerations of wall slip boundary condition as well as no-slip boundary condition. For the sake of generalized memory effects, mathematical fractional models are formulated based on Caputo, Caputo-Fabrizio, CPC, Atangana-Baleanu in Caputo sense and Prabhakar fractional operator with generalized Fourier’s law and Fick’s law. These fractional models have been solved analytically and exact solutions for dimensionless velocity, concentration and energy equations are calculated in terms of special functions by employing the Laplace transformation method. To comprehensively discuss the dynamics of the considered problem, physical impacts of different parameters on momentum, heat and mass profiles are studied and reverberations are graphically highlighted and deliberated. Special cases are investigated of the obtained solutions and it is noticed that some well-known results are achieved, found in the literature from these special cases. Thermophysical investigation of Oldroyd-B fluid with functional effects of permeability along with memory effect study using non-singular kernel derivative approach. Double diffusive magneto-free-convection flow of rate type fluid over a vertical plate with heat and mass flux, special functions based analysis using local and non-local kernels subject to exponential heating. Functional effects of permeability on Oldroyd-B fluid under magnetization, a comparison of slipping and non-slipping solutions. Fractional analysis of MHD Maxwell fluid with ramped boundary conditions and transport phenomena solutions based on special functions. Thermal and concentration diffusion impacts on MHD Maxwell fluid with generalized Fourier’s and Fick’s perspective. Special functions based solutions of unsteady convective flow of a MHD Maxwell fluid for ramped wall temperature and velocity with concentration. Mittag-Leffler form solutions of natural convection flow of second grade fluid with exponentially variable temperature and mass diffusion using Prabhakar fractional derivative. Heat and mass transport impact on MHD second grade fluid together with a comparative analysis of fractional operators. Generalized Mittag-Leffler kernel form solutions of free convection heat and mass transfer flow of Maxwell fluid with Newtonian heating by applying Prabhakar fractional derivative approach. Various fluid models that are mentioned above, exact solutions are derived and the solutions presented in all the fluid models satisfy the imposed initial and boundary conditions. A comprehensive comparative studies between fractional and non-fractional models describes that the fractional model elucidate the memory effects more efficiently.
Applications of ternary nanoparticles to heat transfer flow of Casson fluid
(UMT Lahore, 2022) Rizwan Karim
This thesis deals with the modeling issues of transport problem with fractional operator. The fractional model with generalized Fourier’s law is discussed for Casson fluid flow over a flat surface. The dimensionless governing model is solved with Laplace transform method and the different comparison are plotted from the obtained solutions. Other feature of the problem has been analyzed instead of the symmetric behavior of the properties for different values of fractional parameter. As a result, it is found that ternary nanoparticle decays faster than the hybrid and mono nanoparticle. Further, it is evident that law based fractional model is more accurate and efficient in fitting any experimental data instead of artificial replacement.
Best proximity points of generalized contractions in ordered b-quasi metric spaces
(UMT Lahore, 2022-12-29) Hira Yousaf
The motive of this dissertation is to explore the existence of best proximity points for more general contraction conditions in the context of b-quasi metric spaces. Czerwik introduced b-metric space which is more general than metric space. Many authors generalized metric space and quasi metric space. A quasi metric space is a distance function which is asymmetric unlike the metric which is symmetric. Apart from generalization of metric space, quasi metric space induce a partial order, which is an important tool for mathematics and related discipline. In this study, the first part consists of a review of some ordered rational proximal contraction type results for the sake of completeness. In the second part we introduced generalized rational proximal contraction in the frame of references of b-quasi metric space. Results presented in this thesis generalized and extended many results in existing literature. Our results extend many best proximity point theorems on partially ordered b-quasi space including the well known banach contraction principal. We present some examples to manifest the generality of our conclusion.
Computational analysis for bioconvection of motile microorganisms in prandtle nanofluid flow across an inclined sheet
(UMT Lahore, 2022) Muhammad Ajmal
In the existence of an aligned magnetic Öeld across the inclined stretching shrinking sheet in non-darcy permeable medium,the two dimensional boundary layer áow of prandtl nanoáuid is analyzed. The formulation of partial di§eren- tial equation, which manage the distinctive properties of heat and áow transfer is converted into ordinary di§erential equation by using the appropriate similarity variables. The governing equations are resolved numerically by using the Runge- Kutta method along shooting technique is coded in MATLAB platform.This pro- cedure is widely used for the solution of such problems as it is e¢ cient with cost- e§ectiveness and Öfth order accuracy. The signiÖcance of immerse parameters on the velocity,temperature,concentration and bioconvection are dispose through Ög- ures.Also physical parameters skin friction coe¢ cient and nusselet numbers are demonstrated in table.The declining behavior of the áow velocity against the áuid parameter 1 and the porosity parameter KP and the local inertia coe¢ cient F r these two parameters of Darcy resistance and Darcy forchiemer resistance are responsible for slowing the áuid speed .The áuid temperature is increases with pa- rameters of Brownian motion N b and thermophoresis N t. The increasing values of Brownian motion N b and the Lewis numberLe decreases the concentration of nanoparticles. The ináated inputs of Lewis numberLb and the Peclet number P e declined the bioconvection distribution
Conformal compact model of massive stellar object in 𝒇𝒇(𝑹𝑹, 𝑻𝑻) gravity
(UMT Lahore, 2022-07-19) Ghulam Fatima
The present analysis explores exact solutions of a massive compact stellar object in f (r, t ) gravity using conformal motion. here r is ricci scalar and t is trace of energy momentum. we presume that the substance inside the stellar structure has high pressure and density as well as strong gravitational fields. the integral relationship between metric functions is due to conformal motion. we apply the conformal motion to obtain an anisotropic solution of the f (r, t ) field equations. for relativistic compact stars, this approach is very useful. for the stellar object p srj1614 − 2230 we discuss radius, mass, density, pressures, energy conditions and stability criteria. our solutions have been seen to be physically acceptable in f (r, t ) using conformal motion.
Connection number based topological indices of certain nano structures
(UMT Lahore, 2022) Nafisa Tahir
Let G = (V (G), E(G)) be a simple undirected, finite, and un-weighted graph with the vertex set V (G) and edge set E(G), E(G) (V (G) × V (G). If Ʈ is a collection of the aforesaid graph, then a mapping Top: → ℜ is called a topological indices, that assign some real numbers to each member of Γ with the help of vertices or degree between them. Moreover, if G1 ≃ G2, then Top(G1) = Top(G2). In this thesis, we obtain connection based Multiplicative Zagreb indices of some nanostructures such as, 1st connection Zagreb index, 2nd connection Zagreb index, and 3rd connection Zagreb index. At the end, all the expressions are obtained from 1st; 2rd; 3rd connection Zagreb indices of the some nano structures.
Cracking of charged compact star admitting conformal motion
(UMT Lahore, 2022) Adnan Amin
The cracking of charged spherically symmetric compact star admitting conformal motion is examined in this thesis. It is supposed that the stellar structure’s interior is going through great pressure and has a powerful gravitational field. An integral interaction between the metric variables is produced by the conformal symmetry requirement. The Einstein-Maxwell field equations are developed, that are further used to construct hydrostatic equilibrium equation. In order to find instabilities in the system when it departs from equilibrium, density dependent perturbation scheme is applied on hydrostatic equilibrium equation. It has been observed that cracking occurs in compact star at some points in force distribution from center towards boundary.
Cracking of PSR J1614-2230 with ordinary and dark matter equations of state
(UMT Lahore, 2022) Hafiz Muhammad Saeed
This thesis is kenas to study the ripput of loral density perturbations on spherically symnotne antectropic gravitating system porisining thrwo types of equations of stata, namoly ordinary mattor. bariz matter and admised matter the general framework for perturbation scheme and corresponding equation for distribution of force & developed for considered gravitating source. the devekped framework is applied at an alrezcy developed mode. to icentify cracking points in it. creddag er overturning takes place where rexdied forces switch their sizi iron negative to positive or vice versa. it has been sherwer that cracking te evident in some cases that sugarst tetrament in the model 10 eradicate instabities willen gravitoling syste.
Detection and intensity of tumor cells by graded TOPSIS and graded ELECTRE-I under intuitionistic fuzzy N-soft set
(UMT Lahore, 2022-01-27) Numra Mustara
This study is aimed to determine the most lethal tumor cell and to rank out the tumor cells by graded TOPSIS and graded ELECTRE-I under intuitionistic fuzzy N-soft model. We also present the benefits and applications of both considerate decision making strategies. Furthermore, we compare and contrast the two proposed decision-making techniques. Finally, it will be discussed that which proposed method is preferable in the detection of the most poisonous tumor cell.
Development and analysis of an MCDM problem of residential area selection.
(UMT Lahore, 2022-10-29) Syeda Areej Fatima
Amongst the many reasons why individuals move, the desire for a higher education has historically been the primary driver of migration. Most families in Pakistan move from neighboring towns and cities to Lahore for the higher education of their children, due to the fact that Lahore is known as the "City of Colleges." It could be challenging to select a home with the optimum amenities as they are unsure of which area offers the best utilities as well as the shortest distance between the chosen educational institution and the residential areas. The problem of choosing the most suitable residential area according to a specific educational institution, is handled by the process of mathematical modeling, resulting into a multi criteria decision making (MCDM) model. The data is collected with the help of a famous website as well as the survey on different parameters of the problem. Based on this information, a decision table is constructed. The resulting MCDM problem is solved with the help of MCDM techniques, AHP and Fuzzy TOPSIS. AHP is applied to obtain criteria weights, whereas Fuzzy TOPSIS is employed to obtain the ranking of the alternatives. For this research problem, formulas, methods, and procedures utilized in Fuzzy TOPSIS and AHP have been addressed, and for better understanding of the results, the acquired results have also been graphically depicted. Fuzzy TOPSIS programming has also been made available to increase the magnitude of the job.
Development of distance measures for cubic intuitionistic fuzzy hypersoft set with application.
(UMT Lahore, 2022-02) Misbah Khalid
Cubic intuitionistic fuzzy set (CIFS) was introduced by Kaur and Garg in 2018. It was efficiently used to solve unpredictability by describing them into membership and non-membership intervals, also membership and non-membership values. In this study, we hybridized the notion of CIFS with soft set (SS) then expand it, to the Cubic Intuitionistic Fuzzy Hypersoft Set (CIFHSS) which deals with multiple distinct attributes in the cubic set environment. Initially we introduced the concept of internal CIFHSS and external CIFHSS, developed different aggregation operators as P-cubic (resp. R-cubic) IFHS subset, P-union (resp. P-intersection, R-union, R-intersection) of cubic intuitionistic fuzzy hypersoft set. Furthermore, complement of CIFHSS is also discussed with the examples. In the end we found the different distance measures and used these distance measures in decision making process.
Development of hesitant fuzzy hypersoft set and its application in decision making.
(UMT Lahore, 2022) Muhammad Zafarullah
Multi-criteria decision-making problems are concerned with coordinating and taking care of matters of preferences and preparations. Molodtsov’s soft set theory is newly emerging mathematical approach to handle uncertainty. Adem Yolcu and Taha Yasin Ozturk introduced the concept of fuzzy hypersoft set in March 2021. But fuzzy hypersoft environments cannot be used to solve certain type of problems in which the attributes values contain hesitancy in their membership values against the alternatives. In this work, we introduce a hybrid structure named hesitant fuzzy hypersoft set which is a combination of hesitant fuzzy set and hypersoft set. Then, we define operations on hesitant fuzzy hypersoft sets. A real-life multi-criteria decision-making (MCDM) problem is modelled by using the concept of hesitant fuzzy hypersoft set and solved by TOPSIS to obtain the ranking of alternatives. The results are quite promising and fulfil the need of the problem in hand. The proposed concept can be applied in medical diagnosis, pattern recognition etc.
Dynamics of cavity evolution in cluster of stars and 𝒇(𝑮, 𝑻) gravity
(UMT Lahore, 2022-03) Imdad Hussain
The role of this thesis is to analyze the evolution of cavities for cluster of stars in context of modified Gauss-Bonnet gravity. For this purpose, we consider the spherically symmetric geometry with locally anisotropic fluid distribution. It is assumed that the proper radial distance among neighboring stellar components stays unchanged during purely areal evolution stage. We provide some analytical solutions by using general formulism in f (G, T ) gravitation theory.
Exact traveling wave solutions possessing beta derivative of the fractional generalized reaction duffing model and the density dependent fractional diffusion reaction equation
(UMT Lahore, 2022) Kausar Shahzadi
In this dissertation, we study the two important nonlinear fractional differential equations, beta derivative the generalized reaction duffing model and density dependent m- fractional diffusion reaction equation by using three dependent, generalized tanh method method, generalized bernoulli sub-ode method and generalized Bernoulli sub-ode method. A wave transformation in the fractional form via the beta derivative is applied to transform the differential equations into ordinary differential models. These methods contribute a variety of exact solutions. As a result, a series of exact traveling wave solutions are obtained by using the software mathematica. The numerical simulation of obtaining solutions depicts that the suggested approaches are simple and efficient to produce rapid results as compared to many other methods.

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