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Item Groundwater flow analytical and numerical solutions(UMT Lahore, 2021) Asima RehmanGroundwater flow models which can be used to determine the aquifer hydraulics of an artificially recharged aquifer of Windhoek in Namibia are investigated. The geology of this aquifer is very complex and heterogeneous, due to the presence of various and randomly distributed fractures and faults as well as the variations in the mineral composition of the water-bearing pure quartzite and micaceous quartzite. Water storage occurs within these rocks and fractures, causing the aquifer to be categorized as a double porosity type aquifer. The flow of the injected water within the Windhoek aquifer has been analyzed using the Forchheimer and Darcy’s law equations. In this study the flow was evaluated in one dimension. Therefore, to replicate the flow of water within a double porosity aquifer, various types of differential operators were applied to these flow equations. Consequently, two distinct models were developed. The first one is based on the classical differentiation as it does not consider the heterogeneity of the geological formations; hence the Laplace transform operator has been utilized to derive the exact solution to this effect. The second model is based on the nonlocal differential operator which has the ability to incorporate the effect of long-range dependency that is expressing memory effect into the mathematical formulation. Therefore, the approximate solution in this case has been derived using numerical methods such as the Adams-Bashforth and the Newton polynomial (Atangana-Seda) schemes. The classical numerical simulations depicted a normal flow when the fractional order was equal to 1; and this defines a flow within a homogeneous medium. Whereas, the model developed using fractional derivative depicted two flow scenarios namely the fast flow and the slow flow; observed when the fractional order was smaller and closer to 1 respectively. Thus, the fast flow has been attributed to the flow within the pure quartzite where the permeability and porosity are considered very high. Moreover, the slow flow has been attributed to the flow occurring in the micaceous quartzite; which has less permeability and low porosity due to less degree of fracturing and increasing mica content in the rock.Item Polynomial based topological indices of pent-heptagonal nanosheets(UMT Lahore, 2021) Hafiza Bushra MumtazThe combination of chemistry, mathematics and information science leads to a new subject called cheminformatics. It studies the quantitative structure–activity and quantitative structure–property relationships that are used to predict the biological activities and properties of chemical compounds. In this thesis we introduce different types of topological indices to study the chemical structures, including first Zagreb index, second Zagreb index, modified second Zagreb connection index, general Randic index, symmetric division index, harmonic index, inverse sum index and augmented index. We use these M-polynomial-based topological indices to study the pent-heptagonal nanosheets of VC₅C₇ and HC₅C₇, and examples are also presented to strengthen the main results of the thesis work.Item Analysis of non-linear fractional partial differential equations through analytical approach(UMT Lahore, 2021) Waqas Ali FaridiThe main aspire of this desertion is to analyze the partial differential equations with the new extended direct algebraic scheme, and extended (g′/g²)-expansion algorithm in analytical perspective and also mathematical modeling of biological disease in sense of fractional calculus. We analyzed and established novel soliton solutions for different types of partial differential equations in which non-linear directional couplers with the optical meta-materials, the space-time fractional non-linear phi-4 equation, an improved perturbed Schrödinger equation with Kerr law non-linearity in non-linear optics, and the fractional time-space non-linear biological population model. The partial differential equations are reshaped utilizing the different fractional-order derivatives. The soliton solutions of the considered partial differential equations are determined as rapidly convergent sequences with effectively computed by utilizing Mathematica software. The obtained solutions sets are more generalized than the existing solutions as it is transformed into fractional-order derivative because it gives the solutions of problems with heavy tails or infinity fluctuations. Furthermore, the obtained solutions contain almost all types of solitons such as dark, bright, dark-bright, rational, periodic, breather, and singular soliton solutions, etc. The graphical interpretations of obtained solutions are also depicted by allocating the feasible values to unknown constant parameters.Item Numerical modeling of susceptible infected epidemic model of HIV/AIDS disease(UMT Lahore, 2021-02-04) Iqra AfzalIn this academic research study, pandemic models of HIV/AIDS have been thoroughly analyzed to their respective core. Consequently, the significance of the awareness creating programs have been investigated with reference to their association and ultimate impact on outbreak of these pandemics. This study is solely focused toward ascertaining the fate of the proposed research hypothesis, which argues that introducing the awareness and developing the consciousness among people regarding safe practices will tend to encourage people to adopt these practices. Henceforth, this improved cognizance will lead to comply with the safe practices and eventually, the transmission rate of virus within population will portray momentous fall. Analysis of this model has efficaciously exhibited that awareness-developing programs appears to be an apropos approach for controlling the spread of the virus and correspondingly casts an affirmative affect in reduction of infection prevalence of the infectious population. This model has been analyzed with the application of stability theory, which is a noteworthy component of the differential equations process. Here, three different deciphering techniques have been deployed to solve out this model, namely Forward Euler, RK-4 and Proposed Finite Difference (NFSD). The NFSD approach appeared to be more reliable numerical technique than the other two methods since it demonstrated most accurate and precise outcomes. Not confined to aforementioned remarkable distinction, the proposed finite difference technique also possesses all the mandatory features of HIV/AIDS model. including positivity, equilibrium stability and independence of time step size, which is an idiosyncratic limitation of Forward Euler and RK-4 methods.Item M-polynomial based topological indices of planar cellulose networks(UMT Lahore, 2021-03-31) Fida ShafiqueThe combination of chemistry, mathematics and information science leads to a new subject called as cheminformatics. It studies the quantitative structure activity relationship (QSAR) and quantitative structure property relationship (QSPR) that are used to predict the biological activities and properties of chemical compounds. In this thesis, we calculate the M-polynomial of planar cellulose networks and use these polynomials as a latest developed tool to compute the certain degree-based topological indices such as first Zagreb, second Zagreb, general Randic, reciprocal general Randic, symmetric division degree index, harmonic index, inverse sum index and augmented Zagreb index. Examples are also presented to strengthen the main results of this thesis work.Item A study on spherical fuzzy hypersoft set and its applications(UMT Lahore, 2021) Misbah Ur Rehman SiddiquiThere are many real-life decision-making problems that may not be completely modeled and solved by using the concepts and techniques based on fuzzy set, intuitionistic fuzzy set, picture fuzzy set and soft set. There exists a constant need to coin new mathematical structures to address the decision-making problems of the modern world to fulfil the needs of the society. In this work, we introduce a concept which is the combination of spherical fuzzy set and hypersoft set, termed as spherical fuzzy hypersoft set (SFHS). It elaborates the division of positive membership, neutral membership and false membership. It also helps us to solve the real life problems that were not fully solvable in spherical fuzzy set and hypersoft set based environment when discussed separately, but become solvable in spherical fuzzy hypersoft set (SFHS) environment. The concepts of the subset of SFHS and the equivalence of two SFHSs are also defined. For the implementation of newly proposed mathematical structure, a real-life application problem is modeled into a multi-criteria decision-making (MCDM) problem and a well-known MCDM technique, known as TOPSIS, is implemented and the concept of SFHS is induced in the algorithm of the method. The results align with the requirements of the applications problem. The results are demonstrated graphically to completely understand the importance of the study. Moreover, the formulas of the distance and similarity measures on SFHSs are also developed and utilized to solve a real-life decision-making problem. The results obtained in the study are quite fruitful and these concepts may be extended to AI based decision making, machine learning, deep learning, pattern recognition, medical diagnosis and related areas.Item Core envelope mathematical model of super dense stars(UMT Lahore, 2021) Ghulam AbbasIn this study, the core envelope model of anisotropic spherically symmetric super dense compact star is developed. In this development, the core is expressed with a linear equation of state (EOS) and the envelope is outfitted with the generalized polytropic EOS. All the geometrical and physical variables are viable for the core and envelope of the star. The junction conditions are also satisfied for the three regions i.e. the core, envelope and the outer space. The developed model is in great agreement with the realistic stars Vela X-1, Her X-1 and SMC X-1. It is concluded that core of the star compresses as the mass increases, justifying the dominating effect of gravity of astronomical objects with greater masses.Item Influence of slip and fractional parameter on transport phenomena of a viscous fluid(UMT Lahore, 2021-02) Fareeha RanaThe present study deals with slip effects on viscous fluid containing nanoparticles. The control partial differential equations of nanofluids are modeled by applying Caputo, Caputo-Fabrizio and ABC fractional derivatives. The solution of energy and momentum equation is balanced in the form of a series. By using Laplace we have obtained the exact solution of the fractional control derivative fluid concentration, temperature, velocity field. We took the results by solving the numerical calculation and illustrate the result in the graphical form. For various suitable physical parameters, such as α, η fields are presented graphically.Item Anisotropic compact star core- envelope model with linear core and van der waals envelope(UMT Lahore, 2021) Hira AkbarIn this research an anisotropic spherically symmetric core envelope model of a super dense compact star is developed. The core is represented by a linear equation of state (EOS), whereas the envelope is equipped with Van der Waals EOS. In the core and envelope of the star, all geometrical and physical factors are viable. The three regions, i.e. the core, envelope and outer space satisfy the junction conditions. The proposed model validates with the properties of the neutron stars: Vela X-1, Her X-1 and SMC X-1. It is concluded that core of the star compresses as the mass increases, justifying the dominating effect of gravity of astronomical objects with greater masses.Item Approximate solutions of the flow models for non-newtonian fluids using hybrid techniques(UMT Lahore, 2021) RoomanThis thesis deals with the applications of a novel hybrid scheme to find the approximate solutions of non-newtonian fluids under different circumstances involving fractional derivatives. Using mongrel approach, we have less calculating efforts and time consumption as compared to other methods present in the literature to find the solutions of problems. In starting, some preliminaries and basic concepts related to newtonian and non-newtonian fluids, constitutive equations, fractional calculus and mongrel scheme have been presented. Then in the next chapters the mongrel scheme has been successfully applied to find the approximate solutions of second grade and maxwell fluids with non-integer order derivatives. In chapter 2, approximate solution of unsteady rotational flow of second grade fluid with non-integer caputo time fractional derivative through a circular cylinder has been procured. The flow of the fluid is generated due to hyperbolic stress applied on the surface of cylinder. The laplace inversion numerical algorithms methodology is adopted to solve the governing equations. The inverse laplace transformation has been procured through stehfest’s’ algorithm using mathcad software. The affirmation of the numerical results in inverse laplace transform is executed by using four other numerical inverse laplace algorithms namely, tzou’s algorithm, honig and hirdes algorithm, fourier series algorithm and talbot’s algorithm. Towards the end, the velocity field and shear stress graphs are depicted to understand the response of physical parameters. The aim of chapter 3 is to examine the flow of maxwell fluid involving fractional time derivatives in an infinite long circular cylinder. A mongrel scheme is used to achieve semi-analytical solutions. The fluid is lying inside the cylinder. The approximate results for the velocity field and the time dependent hyperbolic shear stress have been created. The approximate solutions are procured by employing laplace inversion stehfest’s algorithm using mathcad software. The affirmation of the numerical results in inverse laplace transform is executed by employing several other numerical inverse algorithms namely as tzou’s algorithm, honig and hirdes algorithm, fourier series algorithm and talbot’s algorithm. At the end, velocity field and time dependent shear stress graphs are plotted to see the insight behavior of physical parameters and discussed in detail.Item Analysis of unsteady flow of a Burgers’ fluid with Caputo time fractional derivatives(UMT Lahore, 2021) Mubeen ZafrullahThis dissertation deals with the applications of a new hybrid scheme to find the approximate solutions of non-Newtonian fluids under different circumstances involving fractional derivatives. using hybrid approach, we have less calculating efforts and time consumption as compared to other methods present in the literature to find the solutions of problems. in starting, some preliminaries and basic concepts related to Newtonian and non-Newtonian fluids, constitutive equations, fractional calculus and hybrid scheme have been presented. then in the next chaptes the mongrel scheme has been successfully applied to find the approximate solutions of unsteady longitudinal flow of burger’s fluid with non-integer caputo time fractional derivative through a circular cylinder. the flow of fluid is generated due to hyperbolic stress applied on the surface of cylinder. the laplace inversion numerical algorithms methodology is adopted to solve the governing equations. the inverse laplace transformation has been procured through stehfest’s’ algorithm using MATHCAD software. the affirmation of the numerical results in inverse laplace transform is executed by using the four other numerical inverse laplace algorithms namely, tzou’s algorithm, honig and hirdes algorithm, fourier series algorithm and talbot’s algorithm. towards the end, the velocity field and shear stress graphs are depicted to understand the response of physical parameters.Item M-polynomials and degree based topological indices of pseudo-regular graphs(UMT Lahore, 2021) Kashif JavedIn my this work I have computed the topological indices like first Zagreb, second Zagreb, second modified Zagreb, general randic, and symmetry division degree (SDD), harmonic index (H), inverse sum index (IS), and augmented Zagreb index (AZI) of particular three types of Pseudo regular graph with the help of M-polynomialsItem Radiative heat and mass transfer analysis in main stream velocity which oscillates without reversing(UMT Lahore, 2021) Khushbakht NaseerWithin recent work the phenomenon of mixed convective heat and mass exchange/transfer in free stream which oscillates without turning over the semi-endless vertical heated plate ( y = 0 , x ≥ 0) within the sight of thermal radiation is investigated.fluid under consideration is viscous, incompressible and optically dense grey. The temperature of the plate is uniform and greater than that of oncoming fluid. In this analysis the free stream velocity is of the form U (x, t) = Uo(x)V (ωt) = Uo(x)(1 + α1sinωt), where 0 ≤ α1 < 1 is the amplitude parameter, Uo(x) ∝ xn, and 0 ≤ n < 1. Three cases for n = 0 (level plate), n = 1 3 (wedge of semi-vertex angle 1 4 π) and n = 1 (stagna- tion point) are discussed. A gathering of transformations is introduced to decrease the boundary layer equations to advantageous form of the equations for integration . The solutions of the transformed model are obtained by employing the asymptotic expansions for the small and large values of the frequency parameter 1 = ωx Uo(x) . The effect of involved dimensionless parameters such as Richardson number, Mod- ified Richardson number, Prandtl number and Schmidt number is analyzed. Main aim of this study is to analyze the composite matching of inner and outer solutions to observe the behaviour of radiative heat and mass transfer in free stream which oscillates without reversing.Item Application of Summudu transformation to unsteady differential type fluids flow(UMT Lahore, 2021) Muhammad ShakarIn this dissertation, the problems of unsteady unidirectional flow of second grade fluid are developed. The governing equations of flow are modeled. By using summudu transform, analytical solutions of modelled equations are developed for the following problems: (i) unsteady couette flow, (ii) unsteady flow for rigid and free boundaries, (iii) flow between two parallel plates suddenly set in motion with same speed, (iv) unsteady poiseuille flow, (v) unsteady generalized couette flow and (vi) unsteady generalized couette flow for rigid and free boundaries. Since the summudu transform has units preserving properties, therefore aforementioned problems are solved without restoring the frequency domain. Further, the solutions for the velocity fields that have been obtained; have complete agreement with those established by using the laplace transformation. Moreover, the corresponding solutions for newtonian fluids can be obtained as limiting cases for small time of our solutions. Expression for velocity, volume flux and frictional force are obtained for both large and small times. Finally. the influence of the pertinent parameters on the velocity of fluids is also analyzed by graphical illustrations.Item Analysis of mhd third grade fluid flows through an inclined channel with ohmic heating.(UMT Lahore, 2021) Muhammad SajidIn this dissertation, we investigated the MHD flow of a third grade fluid through an inclined channel. The fluid is incompressible and electrically conducting with the heat transfer in the existence of a uniform magnetic field. Three different problems namely, plane Couette flow; Poiseuille flow and Couette-Poiseuille flow have been discussed. In each case, the nonlinear equations governing the flow and heat transfer are solved for velocity and temperature pro- files by employing the regular perturbation method, Homotopy perturbation method and Homotopy analysis method, and for numerical solutions bvp4c technique built-in MATLAB is used. Finally, the effects of magnetic parameter, gravitational parameters and brinkman number are analyzed for velocity and temperature profiles and the results are pre- Sented through graphs and in tabular forms. Further, we compare our obtained semi-analytical and numerical results in graphical and tabular forms.Item Leap Zagreb, leap hyper Zagreb and generalized leap Zagreb indices of some convex polytops and their polynomials(UMT Lahore, 2021) SanaullahIn this thesis, we compute first, second and third leap Zagreb indices first, second leap hyper Zagreb indices and general first, second leap Zagreb indices of convex polytopes. We also compute first, second leap Zagreb polynomials and first, second leap hyper Zagreb polynomials for the same convex polytopes.Item Study of compact massive anisotropic stellar in high curvature gravity(UMT Lahore, 2021-02-20) Ansa SultanaThis thesis devoted to study dynamical characteristics of compact massive objects via embedding in the frame work of f (R) gravity. It is proposed there is a basic distribution of anisotropic fluids in action with a set of metrics that is physically appropriate potential for eλ. The model parameter focus on four constants ̄a, ̄b, C and D whereas the solutions actually depend upon two free constants as the four constants are highly correlated. The chosen model of anisotropic compact object satisfies all the required physical specifications which are investigated using table illustration, where −200 < n < 200. We find that the models of compact massive objects in higher curvature gravity is highly controlled by the effects of f (R) dark source terms.Item Image encryption algorithm based on Bernoulli chaotic map(UMT Lahore, 2021) Kiran AftabCurrently, one thing that is very important is that we secure the images. For this purpose, we prompted another method for picture securing which is a more protected and fast method. In this thesis research, we introduced a new encryption algorithm that depends on the Bernoulli map. In this method, we create iteration and apply permutation for better encryption results and for improving the image securing system. Then we perform different analyses for checking the security and performance of this encryption method.Item Numerical analysis of delayed MSLIR epidemic model of HBV disease dynamics(UMT Lahore, 2021-12-16) Muhammad KazimThis thesis involves numerical solution of nonlinear delayed Immunized Susceptible Latent Infected Recovered (MSLIR) epidemic model of HBV disease. The dynamics involved in the transmission of HBV is mathematically formulated with considerations of different populations of individuals. This model is solved numerically with three different numerical techniques: forward Euler, RK-4, and the proposed non-standard finite difference (NSFD) techniques. The proposed (NSFD) technique becomes more efficient and reliable numerical technique than forward Euler and RK-4 technique. NSFD technique retains all essential characteristics of continuous (MSLIR) HBV epidemic model like positivity, stability of equilibrium, while well-known forward Euler and RK-4 cannot sustain these characteristics. Furthermore, the proposed technique is independent of time step size, while forward Euler and RK-4 depend on time step size. The numerical simulations with the aid of a numerical is presented for the validation of all traits. The model in this study is based on the standard SEIR model.Item Reverse topological properties of convex polytopes and their line graphs(UMT Lahore, 2021) Bushra IshaqIn this thesis, we will compute total reverse vertex degree index, first reverse Zagreb alpha index, first and second reverse Zagreb and hyper-Zagreb indices, reverse atom bond connectivity index, reverse geometric arithmetic index, sum connectivity reverse index, product connectivity reverse index, first and second reverse Zagreb polynomials and reverse hyper-Zagreb polynomials for convex polytopes Rn, Sn, Qn, Tn and Dn. We did same for line graph of these convex polytopes.