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Item Generating solutions for charged stellar model in f(R) theory(UMT Lahore, 2023) Amir FarooqThe main purpose of this work is to develop a general framework for generating solutions of charged stellar models in f(R) theory of gravity with class one metric. The relation of the anisotropy factor, which depends on radial and tangential pressure, serves as a main source of generating solutions. The linear equation of state and conformally flat condition for class one metric are used to develop a consistent system of differential equations. We conclude that it is possible to develop generating solutions with charge for the system in f(R) gravity.Item Thermodynamical analysis of MHD flow of generalized second grade fluid by using some fractional derivatives.(UMT Lahore, 2023) Ahmad RazaThe objective of the current work is to use the fractional derivatives of Caputo, Caputo-Fabrizio and Atangana-Baleanu-Caputo (ABC) to model the heat transition of a second-grade fluid. The flow is examined as a result of magneto hydrodynamics (MHD), heat transfer and mass profile. The motion of the infinite vertical plate is more broadly time dependent. Additionally, we are considering the exponential heat phenomenon when it comes to the infinite plate’s thermal properties. The set of dimensionless fractional governing equations, which includes the heat, mass, momentum and energy equations subject to boundary and initial conditions, by employing the Laplace transform method allows for a precise analytical solution. Graphical plots of solutions are used to examine how various parameters, such as the fractional parameter α, thermal and mass Grashof numbers Gr, Gm, Schmidt number Sc and Prandtl numbers Pr, affect the physical behaviour of fluid flow, concentration and temperature. Comparison between the temperature, concentration and velocity of fluid through Caputo, Caputo-Fabrizio and Atangana-Baleanu-Caputo (ABC) fractional derivatives is discussed graphicallyItem Analytical solutions of fractional partial differential equations for the second grade fluid flow.(UMT Lahore, 2023) Maira AnwarThis 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.Item Leap Zagreb indices and polynomials of some chemical graphs(UMT Lahore, 2023) Muhammad Jamil NawazIn this thesis, we compute first and second leap Zagreb indices, first and second leap hyper Zagreb indices, and general, first and second leap Zagreb indices of G, S, and Zn. We also compute first and second leap Zagreb polynomials and first and second leap hyper Zagreb polynomials for G, S, and Zn.Item Slip effects on fractional brinkman type hybrid nanofluid.(UMT Lahore, 2023-07-17) Maria IfrahimThis thesis explores the movement of a non-Newtonian fluid containing nanoparticles in a single plate. The flow of the fluid is described using the Brinkman equations, taking into account the presence of a solution. To capture memory effects, a Prabhakar fractional operator is employed. Analytical solutions for the temperature and velocity fields are obtained using the Laplace transform method. The study includes a parametric analysis that visually demonstrates the impact of flow parameters. The findings reveal that the behavior of the fluid is significantly influenced by the presence of nanoparticles. As the fractional parameter increases, two distinct solutions emerge—one for short timescales and another for long timescales. Furthermore, the concentration of nanoparticles exhibits an upward trend with rising temperature and declining velocity. By employing the fractional method, this research provides valuable insights into the analytical solutions, enhancing the interpretation of the results. Moreover, it opens avenues for evaluating potential approximations in future investigations.Item Mostar and irregular indices of line graphs of some classes of graphs(UMT Lahore, 2023) Nimra KhalilIn this thesis, basically we will compute the irregularity indices of para-line graph of certain graphs such as Seirpinski Gasket Sn, Generalised Seirpinski Gasket S(n, C3) and S(n, C4) respectively. Also, we will compute the Mostar index of certain graphs such as line graphs of tadepol, kayak paddle, sunlet and prism graphs.Item Prevalence 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. MushtaqObjectives: 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 uses on screen devices on an average of about 4 or more than 4 hours and having significant forward head posture. Costovertebral angle measured with the goniometer while the chest expansion has been measured with the inches’ tape during respiration and inspiration phases and recorded the difference between them. Results: 54 participants out of 100 confirmed cases of tech neck syndrome have significant reduced chest expansion which is the final result of this study while the 46 participants are having greater chest expansion and showing that they are normal but they have tech neck syndrome.Item Digital color image encryption generated by permutation layer and chen’s hyperchaotic system(UMT Lahore, 2023) Qasim AliData 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.Item Source/sink effect on MHD free convection flow of fractional Casson nanofluid under inclined magnetic field.(UMT Lahore, 2023) Sania SattarThe 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.Item Computing fractional metric dimension of networks under operations(UMT Lahore, 2023) Samreena Qaiser; M. Farhan Tahir; M. MahibGraph 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.Item Forward roll coating of a viscoplastic material onto a porous web(UMT Lahore, 2023) Atika FarooqIn 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.Item Heat absorption effect on MHD free convective flow of fractionalized Jeffrey fluid model.(UMT Lahore, 2023-03-10) Rubina AdreesThe main purpose of this dissertation is to study the time-dependent free convection flow of an incompressible Jeffrey fluid in the existence of magnetohydrodynamic and heat absorption effects across an endless, vertically heated plate with a homogeneous heat flux. In the constitutive equation for heat flow, the Prabhakar-like fractional derivative is utilized. The Laplace transform technique is used to attain the precise solution for momentum and thermal profile. Solutions for the classical case and some well-known results from the literature are retrieved as limiting cases. Moreover, the impact of the flow and fractionalize parameters, α β and γ on the thermal and momentum profiles is graphically highlighted and analyzed. In addition, a contrast between the ordinary model and the Prabhakar-like fractional model is also shown. It is established that the Prabhakar fractional model explains the memory of the physical features of the problem better than an ordinary one. It is discovered that the Prabhakar-like fractional model fits best to describe the memory effect of the thermal and momentum fields. It has been observed that ordinary fluids have a greater velocity than fractional fluids.Item Analytical solutions of non-Newtonian fluid flow containing hybrid nanoparticles with different fractional operators.(UMT Lahore, 2023-07-17) Mubarra AbbasThe present study deals with the fractional model of unsteady and the incompressible MHD Brinkman fluid between vertical plates. For this problem we use the Caputo, Caputo-Fabrizio, Antangna Baleanu and Prabhakar fractional derivatives with suitable boundary conditions. The non dimensional equations solved by Laplace transform method. The solution of energy and momentum are balances in terms of series form. We have also discussed the influence of the memory parameters on the temperature and velocity field. The mathematical outcomes for temperature and velocity field are introduced graphically for different parameters. We also draw some comparisons between different fractional derivatives in order to see more memory of the temperature and velocity.Item Dynamics of tilted massive stellar object in high curvature gravity(UMT Lahore, 2023-07-26) Maria ArshadThe dynamics of Lemaitre-Tolman-Bondi space-time is examined in the setting of a tilted viewer in a form of f(R) gravitation, and a significant connection between tilted and non-tilted observers is found. The addition of the non-universal function of the Ricci scalar in the Einstein-field action concludes to characterize f(R) theory, which stands for accelerated expansion, when determining the updated field equations. Now we determine the role of tilted and non-tilted coherence in the act of dissipative LTB in f(R). Now use kinematical and dynamical variables to discuss the inhomogeneity factors and its growth. It has been discovered that emergence of inhomogeneity factors which depends upon the heat transformation, shear tensor, and addition of scalar for tilted viewer, whereas for non-tilted observers, it depends only on the shear tensor. Additionally, we investigate the non-tilted congruence stability requirements in the presence of dark source terms and indicates that instability of the non-tilted coherence caused by expansion.Item Cracking of stellar configuration with complexity factor(UMT Lahore, 2023-09-15) Fizza IqbalIn this work, the static spherically symmetric stellar system is considered. The main purpose of this work is to check the stability or instability of compact objects under the anisotropic fluid models. We explored different scenarios to configure the stability conditions. A complexity factor is used as an axillary condition. Cracking scheme is used here on compact objects. The hydrostatic equilibrium equation is obtained by manipulating Einstein Field equations. The testing of stability is analyzed by observing change in sign of different physical factors. For this we have used local perturbation scheme for analysis. The compact objects which are taken under consideration are Vela X-1, PSR 1937+ 21 and PSR 31611-2231. Cracking is observed to analyze the stability of CO. We conclude that for taken models, these compact objects are stable at every point and for each value of taken parameter.Item Effect of ternary hybrid nanoparticles on Brinkman type fluid flow between two walls.(UMT Lahore, 2023-07-17) Iram NazThis work provides a unique mathematical framework of ternary nanoparticles for better heat transfer. Ternary nanoparticles are illustrated as this structure has heat conductors. Ternary nanoparticles are made up of three times different groups of nanoparticles that float in a base fluid. In the Laplace transform method and Atangana Baleanu, the fractional order is used to provide a numerical model for both velocity and temperature fields. Ternary nanoparticles are identified as a result, and the heat transfer characteristic is enhanced. Additional ternary experimentation of nanomaterials is animation conducted to achieve a higher temperature transmission. According to the graphed data, ternary nanoparticles exhibit more thermal conductivity than hybrid nanoparticles. As a result, it is discovered that the ternary nanoparticles approach may be used to raise the temperature in comparison to the findings of the most recent published research. Furthermore, the main motivation for this problem is the comparison between the solutions obtained by Fourier’s law and artificial replacement. The Fourier-based fractional approach is more precise and powerful than the artificial approach for modeling heat transfer. Because there is a considerable market need for a cooling agent with enhanced heat transfer qualities, the researchers were inspired to develop a concept that uses existing nanoparticles to improve heat transmission. This approach is very useful in modeling heat transfer problems with fractional operators.Item Modeling of tilted stellar objects in F(G, T) gravity(UMT Lahore, 2023-07-26) Sobia SadiqThe purpose of this effort is to find out role of tilted and non-tilted congruence in the dynamics dissipative Lemaitre-Tolman-Bondi space-time in f(G, T) gravity, where T is stress energy momentum tensor and G represents Gauss-Bonnet invariant. We use kinematical and dynamical variables to discuss the inhomogeneity factor and its evolution. It has been discovered that emergence of the inhomogeneity factor depends upon heat flux, shear tensor, and expansion scalar for tilted observer, whereas for non-tilted observers, it depends upon the shear tensor. Additionally, we investigate non-tilted congruence stability requirements in the presence of a dark source terms and deduce that instability of the non-tilted congruence is caused by expansion. We also observed that Einstein tensor is same for both tilted and non-tilted congruence and energy density is standard for both tilted and non-tilted observer.Item Stability of isotropic stellar object in modified Gauss-Bonnet gravity(UMT Lahore, 2023-06) Aneesa ZulfiqarThe paper explores the stability of isotropic pressure conditions in spherically symmetric dissipative fluid distributions within the context of f(G, T) gravity. We observe that the presence of shear, dissipative fluxes and energy density inhomogeneities in the initially isotropic configuration tends to abandon isotropy leading to pressure anisotropy. For physical significance of the pressure isotropy conditions, we transform the shear-free system into the hydrostatic equilibrium approximation. To strengthen the results, we also explain some arguments by choosing axially symmetric case.Item Computing connection zagreb indices of molecular structures(UMT Lahore, 2023) Alam ShairCA 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.Item Impact of Fractional Derivatives on the MHD Maxwell Fluid Under Different Conditions.(UMT Lahore, 2023) Asma BibiThis thesis investigates entropy generation and heat transfer through natural convection using titanium alloy nanoparticles suspended in water and kerosene. The study uses the external magnetic field and the Laplace inverse transform technique to analyze magnetohydro-dynamic flow through Darcy media. The results show that kerosene-based fluids have greater velocity and temperature profiles than water-based fluids. Entropy generation and begin numbers behave differently near and outside the plate, with increased entropy generation and begin number using different base liquids. The nanofluid volume fraction increases the heat transfer coefficient of both nanofluids, with water-based nanofluids increasing heat transfer coefficients by up to 19.14.