M.Phil / MS
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/52
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item Finite Element Solution of Time Dependent Partial Differential Equation in Structural Dynamics(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Sheer Zaman; CIIT/SP24-RMT-024/LHR; Dr. Muhammad Nauman Bashir; LHR TP 10084This thesis investigates the Finite Element Method (FEM) solution of time dependent Par-tial Differential Equations (PDEs) in structural dynamics, focusing on the transient free vibration of a simply supported elastic cable governed by the one-dimensional wave equa-tion. The primary objective is to numerically model the dynamic behaviour of the structure under various initial conditions and rigorously validate the numerical accuracy, stability, and convergence properties of the selected time integration schemes. The study analysed two distinct vibration modes across three problem configurations: 1. First Mode Vibration (Problems 2 and 3) The cable was initiated in its first mode shape, f(x, 0) = sin(pi*x) and released from rest with a wave speed of c = 2m / s This configuration was analyzed using two explicit time step sizes, k = 0.0495 and k = 0.05 to investigate the critical stability condition. 2. Second Mode Vibration (Problem 1) The string was excited in its second mode shape using prescribed initial displacement and velocity conditions, f(x, 0) = sin(2pi*x) partial f partial t (x, 0) = 2pi * sin(2pi*x) . The wave speed for this case was c = 1m / sItem New Harmonic Multiplicative Fractional Integral Inequalities(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Noor-ul-Ain; CIIT/SP24-RMT-015/LHR; Dr. SAAD IHSAN BUTT; LHR TP 10076In this work, we consider the concept of strongly multiplicatively harmonic convex function (SMHCf ). We establish integral inequalities of Hermite-Hadamard (HH) type inequalities for the product and quotient results, in the frame of multiplicative calculus. We discuss the characteristics of SMHCf function. Further, we derive inequalities of trapezoid and mid- point type. In addition, we also verify the validity of our results by graphical descriptions. Also, we enhance our research by offering various applications to specialfunctions.Item New Multiplicative Fractional Integral Inequalities(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Zain Ali; CIIT/SP24-RMT-018/LHR; Dr. SAAD IHSAN BUTT; LHR TP 10079In the context of multiplicative fractional calculus, we develop new Hermite-Hadamard (HH) type inequalities and present the concept of multiplicative trigonometric exponen- tial convex (MTEC) functions. We investigate their algebraic properties and show how these functions relate to other types of convex functions. Several new fractional HH type inequalities are constructed by employing product and quotient of newly introduced multi- plicative convexities via multiplicative Riemann-Liouville (RL) integrals operator. Further, we derive some fractional auxiliary results of trapezoid and midpoint type and apply our convexities to formulate new bounds. In addition, we also verify the validity of our results by graphical descriptions. We also strengthen our study by providing some applications to special functions.Item Dynamical Stability of Modified Friedmann Equation Through Non-Linear Interactions(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Muhammad Husnain Tariq; CIIT/SP24-RMT-013/LHR; Dr. Shamaila Rani; LHR TP 10074In this thesis, we discuss the dynamical stability scenario in the framework of dynamical Chern-Simons modified theory of gravity. In this regards, we develop six models with nonlinear interactions in the theoretical framework of dynamical Chern-Simons modified gravity and apply the dynamical system analysis to investigate their dynamical stability with phase portraits. These nonlinear interactions are considered through energy conser- vation equations between dark energy and dark matter. We find the dynamical system in terms of autonomous system of differential equations of fractional energy densities of dark energy and dark matter with respect to e-fold number of the universe. This system of equa- tions depends on equation of state parameters related to matter and dark energy and yields the critical points for each interacting model. We consider three cases for matter equation of state as radiation, pressure-less, stiff fluid with various values of dark energy equation of state parameter representing current accelerated expansion of the universe and specific value of interaction parameter. The eigenvalues at each critical point are evaluated and the stability is verified by signs of eigen values. Furthermore, the attractor behavior for sta- ble critical point and repulser behavior for unstable state are discussed through the phase portrait analysis.Item Isotropization and New Solutions for Self-Gravitating Systems with Zero Complexity(2025) Maida Aslam; CIIT/SP24-RMT-021/LHR; LHR TP 10081This thesis explores the compact stellar structure in the context of the F(R,LM,T) gravity theory, employing the Minimal Geometric Deformation (MGD) technique via gravitational decoupling (GD). Starting with the isotropic Durgapal-Fuloria (DF) solution, we construct its anisotropic extension and develop two additional models by imposing vanishing and equal complexity factor conditions. The complexity factor, derived from the Riemann ten- sor’s orthogonal decomposition, serves as a key tool to understand the structural intricacies of self-gravitating systems. The physical viability of the models is tested against observa- tional data from the pulsar PSRJ0740 + 6620, using mass and radius constraints obtained from NICER and XMM-Newton observations. A detailed graphical analysis is conducted to study the radial behavior of energy density, pressure components, and anisotropy, and the parameter space ensuring physical viability is summarized in tabular form for each model.Item ON SOME RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL INEQUALITIES(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Yasmeen Razia; CIIT/SP24-RMT-004/LHR; Dr. Ghulam Farid; LHR TP 10067This paper presents some new extensions of the Riemann-Liouville and Katugampola frac- tional integral inequalities. Tempered fractional operators are incorporated in this study to generalize various results available recently. By replacing classical convexity with the broader concept of h-convexity, more flexible conditions are obtained. Using these as- sumptions, we determine new upper bounds for the so-called tempered fractional integrals. The boundedness of Katugampola fractional integrals is also investigated in detail. These results provide sharper estimates compared to the classical fractional inequalities. The gen- erality of the derived inequalities is further enhanced through exponential tempering. Many existing results are recovered as special cases of our main findings. The obtained inequali- ties unite and further extend several known fractional integral results. The results obtained are useful in mathematical analysis and various applied models. The thesis gives broader and stronger tools to deal with fractional inequalities. It opens new directions for further research in generalized fractional operators.Item Computational Approaches to Connection Number-Based Indices in Metal-Organic Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Abu Harera; CIIT/SP24-RMT-005/LHR; Dr. M. Afzal Siddique; LHR TP 10068Connection number–based topological indices play an important role in chemical graph theory by providing quantitative measures of structural characteristics in molecular and network-based systems. This thesis presents a comprehensive computational study of sev- eral connection number–based indices for metal–organic graphs and their associated line and praline´ graphs. Metal–organic networks are modeled as finite, simple, and connected graphs. For these graphs and their transformations, explicit computational expressions are developed for key connection number–based indices, including the first connection number index, second connection number index, connection number Zagreb indices, modified connection number indices, and selected degree–connection hybrid indices. Closed-form formulas are obtained in terms of fundamental graph parameters such as vertex degrees, connection numbers, and the number of edges. The effect of graph operations, particularly line graph and para line graph constructions, on the behavior of these indices is analyzed in detail. A comparative investigation high- lights how these transformations influence connectivity patterns and structural complex- ity in metal–organic graphs. The results indicate that connection number–based indices are effective in distinguishing structural variations and capturing topological properties of metal–organic networks. The findings of this thesis contribute to the theoretical advancement of connection num- ber–based topological indices and provide useful computational tools for the analysis and modeling of metal–organic structures in mathematical chemistry and related disciplines.Item Thermodynamic Phase Transitions of Black Hole Through Modified Entropy(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Ameer Hamza; CIIT/SP24-RMT-007/LHR; Dr. Abdul Jawad; LHR TP 10070In this thesis, we investigate charged black hole through the framework of Bekenstein- Hawking entropy and modified exponential entropy. These entropies are selected for their direct proportionality to the black hole’s horizon area and its natural derivation from Ein- stein’s field equations. The Bekenstein–Hawking entropy is a universally accepted and geometrically well-defined measure that is directly proportional to the area of the event horizon. On the other hand, the exponential entropy enhances the classical framework by integrating non-extensive and correlation effects inherent to gravitational systems, facili- tating regulated deviations from conventional thermodynamics. These two entropies offer both theoretical precision and practical flexibility in the analysis of black hole thermody- namics. We consider the Davies phase transition formalism, and discuss the stability of a black hole in its respective space and calculate its topological properties for dynamic stability. The expressions for mass, temperature, specific heat and divergence points are calculated. Also, we calculate the winding number an total topological charge with the help of phase portraits to discuss the local stable behavior of under consideration black hole for both entropy expression.Item Inflationary Dynamics within f(Q) Gravity using Non-Abelian Gauge Fields(Library Information Services COMSATS University Lahore Campus, 2023-03-13) Rukhsana Batool; SP22-RMT-038; Dr. Rabia Saleem; LHR TP 8737Within the framework of the f(Q) theory of gravity, we investigated warm inflation using non-Abelian gauge fields. We propose this requirement as the mechanism that terminates the gauge-flation model. For this model, slow-roll parameters and perturbation parameters are presented. We discover the fundamental conditions needed for the slow-roll approxima tion of this model to be realizable. Additionally, we build our model within the context of logamediate and intermediate cases, which, in the Einstein hypothesis, are exact solutions to the inflationary field equation. In terms of the inflaton field, general expressions of the slow-roll parameters, the tensor-scalar ratio, and the scalar spectral index are offered for these two cases. Graphical portrays show that our results are compatible with Planck 2018 data.Item Optical Appearance of Kerr Black Hole Surrounded by Cold Dark Matter(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Sadia Aslam (/FA23-RMT-047); Dr. Rabia Saleem; LHR TP 9790In this work, we provide graphical representation of shadow images of Kerr-like black hole (BH) in the presence of cold dark matter (CDM) halo illuminated with two different accre- tion flow models. The impact of spin parameter a, critical density ρc and the scale radius Rs on the observed images of BHs is carefully addressed. The results indicate that as a in- creases, the circular orbits shifted towards the right, while the larger values of both ρc and Rs caused to enhance the radius of circular orbits of BH shadow. In the case of background light source, the impact of parameter ρc on shadow distortion is extremely negligible, but this influence is relatively small and becomes appreciable when the parameter Rs has larger values. Next, we expand the interior region of accretion disk to the BH event horizon, and consider the motion of particles inside and outside the regions of inner stable circular or- bit (ISCO). The results exhibit that the intensity as well as the radius of BH shadow are gradually increasing with the increase of both ρc and Rs. On the other hand, in the case of retrograde flow, the intensity of the shadow images significantly decreases and a crescent moon emerges in the top of the observer’s frame. Subsequently, we discuss the distinctive features of red-shift configurations for both prograde and retrograde flows. The obtained results interpret that the configuration of red-shifts and the visual signatures is associated to the behaviour of accreting flow as well as with relevant parameters. Finally, using the recent observational data of EHT results, we found the shadow radius of Sgr A∗ provides the best-fit parameter constraints as compared to M87∗.