University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

This paper deals with an SIR model with saturated incidence rate affected by inhibitory effect and saturated treatment function. Two control functions have been used, one for vaccinating the susceptible population and other for the treatment control of infected population. We have analysed the existence and stability of equilibrium points and investigated the transcritical and backward bifurcation. The Pontryagin’s maximum principle has been used to characterize the optimal control whose numerical results show the positive impact of two controls mentioned above for controlling the disease. Efficiency analysis is also done to determine the best control strategy among vaccination and treatment. © 2019, Foundation for Scientific Research and Technological Innovation.

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Applied Mathematics

Fulltext

Differential Equations and Dynamical Systems

Qualitative Analysis and Optimal Control Strategy of an SIR Model with Saturated Incidence and Treatment

ECG graphs are the rough type of graphs which are continuous everywhere but non-differentiable at some points of PQRST complexes of each leads of ECG. These non-differentiable points cannot be interpreted by usual classical calculus but it can be characterized by fractional calculus. In this paper we have applied fractional calculus to distinguish Left Ventricular Hypertrophic ECG from Normal ECG. To interpret the non-differentiable points we have calculated modified left and right Riemann-Liouville fractional derivatives, corresponding Phase Transition(P.T.) values (i.e. difference between left and right modified R-L fractional derivative), mean and standard deviation of the P.T. values at the non-differentiable points of the considerable ECG leads. From the study we observe that the P.T. values are higher for Left Ventricular Hypertrophy cases compared to the normal ones. In addition for LVH patients mean and standard deviation of the P.T. values of considerable ECG leads are higher than those for normal ECGs. This may be a new approach to study any ECG via fractional calculus. © 2018 IEEE.

GENERAL

Proceedings of the 4th IEEE International Conference on Recent Advances in Information Technology, RAIT 2018

Application of fractional calculus to distinguish left ventricular hypertrophy with normal ECG

In this paper we have analyzed a discrete prey-predator model with ratio dependent functional response and linear harvesting rate in terms of the predator species. Algebraically we have discussed the existence of fixed points, their feasibility and stability. Then Neimark-Sacker bifurcation and chaos analysis of the model have been studied algebraically with respect to the hervesting coefficient. By numerical simulation theoretical results have been justied. Finally an idea of chaos control have been proposed. © 2018 IEEE.

Stability and bifurcation analysis of a ratio dependent discrete prey-predator model with linear harvesting

In this paper, we obtain approximate bound state solutions of an N-dimensional fractional time independent Schrodinger equation for a generalised Mie-type potential, namely, V(r(alpha)) = A/r(2 alpha) + B/r(alpha) + C. Here alpha(0 < alpha < 1) acts like a fractional parameter for the space variable r. When alpha = 1 the potential converts into the original form of Mie-type of potential that is generally studied in molecular and chemical physics. The entire study is composed with a Jumarie-type fractional derivative approach. The solution is expressed via the Mittag-Leffler function and fractionally defined confluent hypergeometric function. To ensure the validity of the present work, obtained results are verified with the previous studies for different potential parameter configurations, specially for alpha = 1. At the end, few numerical calculations for energy eigenvalue and bound state eigenfunctions are furnished for a typical diatomic molecule. Published by AIP Publishing.

Journal of Mathematical Physics

Time independent fractional Schrodinger equation for generalized Mie-type potential in higher dimension framed with Jumarie type fractional derivative

In this paper we have studied the effect of the density and temperature of negative ions on the nonlinear dust-acoustic wave propagation in a Lorentzian dusty plasma. We have considered both adiabatic and non-adiabatic dust charge variation. The presence of both low and high populations of negative ions are considered. Separate models have been developed because the two populations give rise to opposite polarity of grain charges. In both models electrons are assumed to follow a kappa velocity distribution while the positive and negative ions satisfy a Maxwellian velocity distribution. Adiabatic dust charge variation shows the propagation of a dust-acoustic soliton in cases of both a high and low population of negative ions whose amplitude depends on the negative ion temperature and negative ion density. On the other hand, non-adiabatic dust charge variation generates a stable oscillatory dust-acoustic shock when the negative ion population is low. An unstable potential has been predicted from this analysis when the negative ion population is high and the dust charge variation is non-adiabatic. © 2018 Cambridge University Press.

Journal of Plasma Physics

Nonlinear dust-acoustic wave propagation in a Lorentzian dusty plasma in presence of negativeions

Klein–Gordon equation is one of the basic steps towards relativistic quantum mechanics. In this paper, we have formulated fractional Klein–Gordon equation via Jumarie fractional derivative and found two types of solutions. Zero-mass solution satisfies photon criteria and non-zero mass satisfies general theory of relativity. Further, we have developed rest mass condition which leads us to the concept of hidden wave. Classical Klein–Gordon equation fails to explain a chargeless system as well as a single-particle system. Using the fractional Klein–Gordon equation, we can overcome the problem. The fractional Klein–Gordon equation also leads to the smoothness parameter which is the measurement of the bumpiness of space. Here, by using this smoothness parameter, we have defined and interpreted the various cases. © 2018, Indian Academy of Sciences.

Pramana - Journal of Physics

Fractional Kleinâ€“Gordon equation composed of Jumarie fractional derivative and its interpretation by a smoothness parameter

In this paper, we have investigated the effect of secondary electron emission on nonlinear propagation of dust acoustic waves in a complex plasma where equilibrium dust charge is negative. The primary electrons, secondary electrons, and ions are Boltzmann distributed, and only dust grains are inertial. Electron-neutral and ion-neutral collisions have been neglected with the assumption that electron and ion mean free paths are very large compared to the plasma Debye length. Both adiabatic and nonadiabatic dust charge variations have been separately taken into account. In the case of adiabatic dust charge variation, nonlinear propagation of dust acoustic waves is governed by the KdV (Korteweg-de Vries) equation, whereas for nonadiabatic dust charge variation, it is governed by the KdV-Burger equation. The solution of the KdV equation gives a dust acoustic soliton, whose amplitude and width depend on the secondary electron yield. Similarly, the KdV-Burger equation provides a dust acoustic shock wave. This dust acoustic shock wave may be monotonic or oscillatory in nature depending on the fact that whether it is dissipation dominated or dispersion dominated. Our analysis shows that secondary electron emission increases nonadiabaticity induced dissipation and consequently increases the monotonicity of the dust acoustic shock wave. Such a dust acoustic shock wave may accelerate charge particles and cause bremsstrahlung radiation in space plasmas whose physical process may be affected by secondary electron emission from dust grains. The effect of the secondary electron emission on the stability of the equilibrium points of the KdV-Burger equation has also been investigated. This equation has two equilibrium points. The trivial equilibrium point with zero potential is a saddle and hence unstable in nature. The nontrivial equilibrium point with constant nonzero potential is a stable node up to a critical value of the wave velocity and a stable focus above it. This critical value increases with increasing secondary electron emission. Thus, in the presence of secondary electron emission, higher velocity shock waves are monotonic. The results have been numerically explained considering the presence of Al2O3 dust grains in the plasma. © 2017 Author(s).

Physics of Plasmas

Effect of secondary electron emission on nonlinear dust acoustic wave propagation in a complex plasma with negative equilibrium dust charge

In this paper we have derived the fractional-order Schrödinger equation composed of Jumarie fractional derivative. The solution of this fractional-order Schrödinger equation is obtained in terms of Mittag-Leffler function with complex arguments, and fractional trigonometric functions. A few important properties of the fractional Schrödinger equation are then described for the case of particles in one-dimensional infinite potential well. One of the motivations for using fractional calculus in physical systems is that the space and time variables, which we often deal with, exhibit coarse-grained phenomena. This means infinitesimal quantities cannot be arbitrarily taken to zero - rather they are non-zero with a minimum spread. This type of non-zero spread arises in the microscopic to mesoscopic levels of system dynamics, which means that, if we denote x as the point in space and t as the point in time, then limit of the differentials dx (and dt ) cannot be taken as zero. To take the concept of coarse graining into account, use the infinitesimal quantities as (Δx)a (and (Δt)a) with 0 < α < 1; called as 'fractional differentials'. For arbitrarily small Δx and Δt (tending towards zero), these 'fractional' differentials are greater than Δx (and Δt), i.e. (Δx)α>Δx and (Δt)α>Δt. This way of defining the fractional differentials helps us to use fractional derivatives in the study of dynamic systems. © Indian Academy of Sciences.

A study of fractional SchrÃ¶dinger equation composed of Jumarie fractional derivative

In this paper, we have investigated an SIR model with logistic growth rate of susceptibles where rate of incidence is directly affected by the inhibitory factors or social or psychological factors. In our model three equilibrium points are obtained, one of them is endemic equilibrium point. One disease free equilibrium points is unstable in nature in all circumstance and the trajectories in the neighborhood of the endemic equilibrium point of our model undergoes a Hopf bifurcation subject to some critical value of the carrying capacity. Finally, numerical solution is done. © Springer India 2015.

Springer Proceedings in Mathematics and Statistics

Bifurcation analysis of SIR model with logistically grown susceptibles and effect of loss of immunity of the recovered class

Modelling of infectious diseaseswas investigated by several authors using mathematical methods. Here, we consider the model in which inhibition effect is taken into consideration in presence of delay of the infected to become infectious. In this model two equilibrium points are found, one is disease free equilibrium point and the other is the endemic equilibrium point. The endemic equilibrium point will exists under certain condition. The character of solutions in the neighbourhood of endemic equilibrium point is directly affected by inhibitory effect. The solutions in the neighbourhood of disease free equilibrium point will be asymptotically stable when the basic reproduction number less than one and the solution in the neighbourhood of endemic equilibrium point will be asymptotically stable when the basic reproduction number greater than one. © Springer India 2015.