https://ir.vidyasagar.ac.in/jspui/handle/123456789/61 Sun, 26 Apr 2026 05:45:02 GMT 2026-04-26T05:45:02Z https://ir.vidyasagar.ac.in/jspui/handle/123456789/6311 Title: A study of some hydromagnetic flow and heat transfer problems with or without hall current Authors: Patra, Ruma Rani Abstract: This study presents the hydromagnetic flow behaviour and heat transfer characteristic under different geometric model. The thesis consists of eight chapters. Chapter 1 presents the definition of key terms, basic equations and a review on earlier works. Except Chapter 2 and 5, all problems are based on time dependent unsteady problems. The induced magnetic field is taken into consideration in Chapter 2 only. Chapter 3 and 4 are designed in rotating frame of reference. The Cogley-Vincent-Gilles heat flux model is adopted in Chapter 2 and 6 while the Rosseland approximation has been considered in Chapter 5. The slip effects on couple-stress fluid over a stretching sheet has been observed in Chapter 5. The impact of Hall current has been explained in Chapter 6 and 7. Impact of convective heating under Arrhenius kinetics on reactive flow has been analyzed in Chapter 4 and 7 where the viscous and Joule dissipations are considered in energy equation. The main findings and some directions for future research work have been summarized in Chapter 8. The momentum equations are solved analytically using the Laplace transform technique(whenever required). The nonlinear partial differential equations are solved numerically using MATLAB software package or by employing the fourth order RungeKutta integration scheme with shooting technique. Velocity field is greatly influenced by magnetic field, rotation, Hall current, radiative heat transfer as well as buoyancy forces. The fluid velocity profile decreases with strengthening of slip parameter while it boosts with increase in Darcy number. The combined effects of suction/injection and convective heating have significant impact in controlling the flow characteristics in the channel. The fluid temperature is increased by Biot number and Eckert number whereas it is decreased by Prandtl number and radiation parameter. The temperature of the reactive fluid reduces with increase in Hall parameter while it increases with suction parameter. The obtained results are validated with previous study and found to be highly satisfactory. Mon, 15 Nov 2021 00:00:00 GMT https://ir.vidyasagar.ac.in/jspui/handle/123456789/6311 2021-11-15T00:00:00Z https://ir.vidyasagar.ac.in/jspui/handle/123456789/6308 Title: Analytical aspects of soft set theory with different real life applications in different directions Authors: Manna, Soumi Abstract: This thesis re ects some tremendous bene ts of soft set theory under di erent uncertain environments (fuzzy, intuitionistic fuzzy, interval type-2 fuzzy, linguistic, complex fuzzy, complex neutrosophic, etc.). It is a combination of total ten chapters where, Chapter 1 is basically the introductory part of the thesis containing some elementary concepts, literature survey and some motivations and objectives behind this research work. Chapter 2 and Chapter 3 are related with fuzzy soft set theory where, Chapter 2 deals with group decision-making problems based on fuzzy soft sets and Chapter 3 deals with some algebraic properties of classical group theory based on fuzzy soft sets. In Chapter 4, we have developed a decision-making approach through soft set theory under linguistic environment by using linguistic scale function. In this Chapter, a new similarity measure for linguistic valued sets has also been introduced via linguistic scale function. After that, in Chapter 5, we have proposed a new generalization of soft set theory named as, generalized trapezoidal intuitionistic fuzzy soft set where, every parameter is in generalized trapezoidal intuitionistic fuzzy sense. Further, we have applied our proposed soft set theory in analyzing the diabetic patient in medical science. In Chapter 6, we have dealt with stochastic multi-criteria decision-making through soft set theory. In this regard, a new concept of trapezoidal interval type-2 fuzzy soft stochastic set has been introduced and discussed. Chapter 7 deals with complex fuzzy soft sets where, similarity measure approach and aggregation operator have been studied under complex fuzzy soft environment. Moreover, in this chapter, a decision-making methodology has been employed for solving problems through complex fuzzy soft sets. In Chapter 8, we have worked on complex neutrosophic soft sets to deal with real-life problems having complex valued truth membership, complex valued indeterminate membership and complex valued false membership. Finally, summary and further research work related to this proposed thesis have been concluded in Chapter 9. Chapter 10 contains some references which have helped to complete this research work. Wed, 22 Sep 2021 00:00:00 GMT https://ir.vidyasagar.ac.in/jspui/handle/123456789/6308 2021-09-22T00:00:00Z https://ir.vidyasagar.ac.in/jspui/handle/123456789/6270 Title: An investigation on m-polar fuzzy graphs and applications Authors: Mandal, Sonia Abstract: In this thesis, di erent types of m-polar fuzzy graphs (mPFGs) have been considered. The major problems considered in the thesis are generalized mPFGs and their properties, operations on mPFGs, degree of vertices of m-polar fuzzy graphs, density of mPFGs, mPF planar graphs, isomorphism and weak self complement mPFGs, edge regular mPFGs, the applications of mPFGs, generalized regular BFGs and product bipolar fuzzy line graphs. This thesis consists of ten chapters. In the rst chapter, the basic de nitions of graph and di erent types of fuzzy graphs which are needed in the subsequent chapters are provided. Also, a history of the problems are cited. In Chapter 2, super-strong and strong mPFV of mPFGs using the concept of strong mPFE are introduced. The strength of connectedness of path etc. are investigated. Also, the strong and strong mPFP are de ned and presented with several properties. Then, an investigation is made on these nodes. An application of strong path problems is also given at the end. In Chapter 3, at rst mPFP, mPFC in an mPFG are de ned. The strength of a connectedness of mPFP is introduced. Next, the strongest and strong mPFP, mPFBs, mPFCNs, mPFT and mPFFs in an mPFG are considered. In Chapter 4, (m-polar fuzzy genus graph) mPFGG is de ned and studied its genus value, strong and weak mPFGG. Also, discussed isomorphism properties of mPFGG. A relation between planarity value and genus value of an mPFG is established. Also, the Euler polyhedral equation is established in terms of the genus value of the mPFGG. Finally, a useful application of mPFGG is given on the topological surface. In Chapter 5, mPF detour g-distance, mPF detour g-interior node, mPF detour g-boundary node are de ned and explained their relations. Also, some properties of these parameters are investigated in detail. In Chapter 6, the connectivity index for mPFG is discussed. The upper and lower boundary of connectivity index for mPFG are presented. If an edge is deleted from a mPFG then its e ects of the connectivity index in mPFG is discussed in this chapter. In Chapter 7, ve new operations on Dombi mPFG, viz. direct product, cartesian product and semi strong product, strong product, lexicographic product are de ned. It is proved that any of the products of Dombi mPFG are again a Dombi mPFG. Next, ring sum, union of two Dombi mPFG are de ned. Then complement and self complement of Dombi mPFG are de ned. And di erent properties on Dombi mPFGs are presented. Finally, Chapter 8, contains some concluding remarks and scopes of further research on the problems that have been studied in the thesis. Mon, 13 Sep 2021 00:00:00 GMT https://ir.vidyasagar.ac.in/jspui/handle/123456789/6270 2021-09-13T00:00:00Z https://ir.vidyasagar.ac.in/jspui/handle/123456789/6259 Title: Some selective studies on Prey-Predator Model under different environments Authors: Roy, Banani Abstract: In this thesis, some prey-predator models have been studied in different environments. Prey-predator relationships are the natural phenomenon of any ecological system. Also, in different environments, behaviors of species are different. In this thesis, those natural phenomenons are discussed by some mathematical models. Firstly, prey-predator three species models have been discussed with vertebral and invertebral predators. Different type functional responses have been considered to formulate the mathematical model for predator and generalist predator. A numerical example has been considered to illustrate the proposed system. The stability of the system has been analyzed using some graphical representations. Then, the effects on prey-predator with different functional responses have been studied. The effects on prey of two predators which are also related in terms of prey-predator relationship has been investigated. Different types of functional responses are considered to formulate the mathematical model for predator and generalist predator of the proposed model. Harvesting effort for the generalist predator is considered and the density dependent mortality rate for predator and generalist predator are incorporated in the proposed model. Local stability as well as global stability for the system are discussed. To evaluate Hopf bifurcation in the neighborhood of interior equilibrium point, different bifurcation parameters have been analyzed. Some numerical simulations and graphical figures are provided to verify our analytical results with the help of different sets of parameters. Also, prey-predator three species fishery model with harvesting including prey refuge and migration have been analyzed. Prey-predator system with Holling type II functional response for the predator population including prey refuge region has been analyzed. Also a harvesting effort has been considered for the predator population. The density-dependent mortality rate for the prey, predator and generalist predator has been considered. The equilibria of the proposed system have been determined. Local and global stabilities for the system have been discussed. The analytic approach is used to derive the global asymptotic stabilities of the system. The maximal predator per capita consumption rate has been considered as a bifurcation parameter to evaluate Hopf bifurcation in the neighborhood of interior equilibrium point. Also, fishing effort is chosen to harvest predator population of the system as a control to develop a dynamic framework to investigate the optimal utilization of the resource, sustainability properties of the stock and the resource rent are earned from the resource. Some numerical simulations have been presented to verify the analytic results; and the system has been analyzed through graphical illustrations. Then a prey-predator model with a reserve region of predator where generalist predator cannot enter have been exemplified. The predator population which consumes the prey population with Holling type II functional response and generalist predator population consumes the predator population with Beddington-DeAngelis functional response. The density-dependent mortality rate for prey and generalist predator are considered. The equilibria of proposed system are determined. Local stability for the system is discussed. The environmental carrying capacity is considered as a bifurcation parameter to evaluate Hopf bifurcation in the neighborhood of interior equilibrium point. Here the fishing effort is used as a control parameter to harvest the predator population of the system. With the help of this control parameter, a dynamic framework is developed to investigate the optimal utilization of resources, sustainability properties of the stock and the resource rent. A numerical simulation has been presented to verify the analytical results and the system is analyzed through graphical illustrations. Also a Holling-Tanner prey-predator model has been considered with BeddingtonDeAngelis functional response including prey harvesting. Gestational time delay of predator and the dynamic stability of time delay preventing system are incorporated into the system. The equilibria of the proposed system are determined and the existence of interior equilibrium point for the proposed system is described. Local stability of the system with the magnitude of time delay at the interior equilibrium point is discussed. Thereafter, the direction and the stability of Hopf bifurcation are established with the help of normal theory and center manifold theorem. Furthermore, profit function is calculated with the help of bionomic equilibrium and it is optimized using optimal control. Some numerical simulations are introduced to verify the validity of analytic results of the proposed model. A prey-predator system with stage structure of predator has been considered. In the proposed model, prey of immature predator and that of mature predator are different. Consumption rate of prey by the immature predator has been described by Holling type II functional response and consumption rate of prey by the mature predator has been described by Holling type III functional response. Both preys obey logistic growth rate. Immature predator transfers to mature predator at a constant rate. Mortality rate of immature predator and mature predator are different. Local stability of the system has been discussed. Transform rate of immature predator to mature predator is considered as bifurcation parameter. Some numerical simulations have been presented to verify the analytic results and the system has been analyzed through graphical illustrations. Key Words: Prey-predator model; Holling type I, type II, type III Functional response; Beddington-DeAngelis functional response; Holling-Tanner Model; Interior equilibrium point; Gestation Time delay; Routh-Hurwitz criterion; Local stability; Global stability; Lyapunov Function; Hopf bifurcation; Harvesting; Optimal control. Thu, 29 Jul 2021 00:00:00 GMT https://ir.vidyasagar.ac.in/jspui/handle/123456789/6259 2021-07-29T00:00:00Z