arXiv subjects

Uttam Ghosh

Publications and source records attributed to Uttam Ghosh.

At least 19 recordsLinked to original sources

arXiv2026

Optimal harvesting under annuity and compound interest laws: economic-ecological trade-offs in a logistic growth model

The relationship between investment policy associated with species growth profile is essential in seeking the most appropriate strategy for a policymaker. Balancing maximum profit with the sustainability of species remains a central issue in both ecological and economic contexts. This study presents a comparative analysis of two interest principles, annuity and compounding, within the framework of optimal control. Various investment policies are examined from the perspective of capital theory, incorporating concepts such as future value, accumulation function, and force of interest, each contributing to the formulation of an optimal control strategy. Our analysis is based on a one dimensional logistic model incorporating linear harvesting. Key parameters include the species growth rate and interest rate, and optimality is evaluated with respect to these variables. Using Pontryagins Maximum Principle, we derive the optimal harvesting policies under both discounting laws and characterize the resulting steady state equilibria. The principal finding indicates that for species with low intrinsic growth rates and low annual interest rates, the annuity law of interest yields optimal outcomes. Conversely, for any annual interest rate, species exhibiting moderate or high growth rates maximize profit under the compound law of interest. The study also addresses maximum net revenue and optimal strategies for varying growth rates under each interest law.

econ.GN↗

arXiv2021

Blockchain Meets AI for Resilient and Intelligent Internet of Vehicles

The Internet of Vehicles (IoV) is flourishing and offers various applications relating to road safety, traffic and fuel efficiency, and infotainment. Dealing with security and privacy threats and managing the trust (detecting malicious and misbehaving peers) in IoV remains the most significant concern. Artificial Intelligence is one of the most revolutionizing technologies, and the predictive power of its machine learning models can help detect intrusions and misbehaviors. Similarly, empowering the state-of-the-art IoV security framework with blockchain can make it secure and resilient. This article discusses joint AI and blockchain for security, privacy and trust-related risks in IoV. This paper also presents problems, challenges, requirements and solutions using ML and blockchain to address aforementioned issues in IoV.

cs.CR↗

arXiv2020

An SDN-IoT-based Framework for Future Smart Cities: Addressing Perspective

In this Chapter, a software-defined network (SDN)-based framework for future smart cities has been proposed and discussed. It also comprises a distributed addressing scheme to facilitate the allocation of addresses to devices in the smart city dynamically. The framework is dynamic and modules can be added and omitted by a centralized controlling unit without disturbing the other components of the framework and other modules may be updated accordingly. In the proposed addressing scheme, a new Internet of Things (IoT) device will receive an IP address from one of their existing neighboring peer devices. This allows devices in the city to act as a proxy and generate a set of unique IP addresses from their own IP addresses, which can then be assigned to new (joining) devices; hence, reducing addressing overhead and latency, as well as avoiding the need to send broadcast messages during the address allocation process. Thus, it achieves considerable bandwidth and energy savings for the IoT devices.

cs.NI↗

arXiv2020

Adaptive Control Plane Load Balancing in vSDN Enabled 5G Network

In this work, we have formulated a controllerhypervisor (C-H) pair deployment approach to provide various network functions (such as differentiation between control and data signals, different translation functions etc.) with low latency. The system model deals with a real network topology and four well defined network latency matrices with an MILP model has been well constructed to optimize latency objectives. Reverse Path-Flow Mechanism (RPFM) has been proposed in order to provide feasible solutions by keeping the network load and link capacity constrained under tolerance limit. We further minimize the H-plane load by distributing the network resources based on the arrival time of SERVICE IN requests from users. Through extensive experiment, the efficacy of the proposed system has been demonstrated in terms of significant latency reduction and an e-ULL (evolved-Ultra Low Latency) experience with efficient handling of all real-time user demands. The proposed approach can be used for similar localization problems like service chain mapping in 5G-NR, baseband unit deployment in 5G C-RAN, firewall deployment in distributed CPS.

cs.NI↗

arXiv2019

Study of memory effect in an EOQ model for completely backlogged demand during shortage

The most commonly developed inventory models are the classical economic order quantity model, is governed by the integer order differential equations. We want to come out from the traditional thought i.e. classical order inventory model where the memory phenomena are absent. Here, we want to incorporate the memory effect that is based on the fact economic agents remember the history of changes of exogenous and endogenous variables. In this paper, we have proposed and solved a fractional order EOQ model with constant demand rate where the demand is fully backlogged during shortage time. Finally, a numerical example has been illustrated for this model to show the memory dependency of the system. The numerical example clears that for the considered system the profit is maximum in long memory affected system compared to the low memory affected or memory less system.

math.OC↗

arXiv2018

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

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 stability analysis of non-hyperbolic equilibrium point has been performed by using Centre manifold theory. 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.

math.DS↗

arXiv2017

The new expansion method to solve Fractional KdV-Equations

Fractional calculus of variation plays an important role to formulate the non-conservative physical problems. In this paper we use semi-inverse method and fractional variational principle to formulate the fractional order generalized Korteweg-deVries (KdV) equation with Jumarie type fractional derivative and proposed a new method to solve the non-linear fractional differential equation named as expansion method. Using this method we obtained the solutions of fractional order generalized KdV. The obtained solutions are more general compare to other method and the solutions are expressed in terms of the generalized hyperbolic, trigonometric functions and rational functions.

math.AP↗

arXiv2017

D Alemberts solution of fractional wave equations using complex fractional transformation

Fractional wave equation arises in different type of physical problems such as the vibrating strings, propagation of electro-magnetic waves, and for many other systems. The exact analytical solution of the fractional differential equation is difficult to find. Usually Laplace-Fourier transformation method, along with methods where solutions are represented in series form is used to find the solution of the fractional wave equation. In this paper we describe the D Alembert s solution of the fractional wave equation with the help of complex fractional transform method. We demonstrate that using this fractional complex transformation method, we obtain the solutions easily as compared to fractional method of characteristics; and get the solution in analytical form. We show that the solution to the fractional wave equation manifests as travelling waves with scaled coordinates, depending on the considered fractional order value.

math.AP↗

arXiv2017

Application of Fractional Derivatives in Characterization of ECG graphs of Right Ventricular Hypertrophy Patients

There are many functions which are continuous everywhere but non-differentiable at some or all points such functions are termed as unreachable functions. Graphs representing such unreachable functions are called unreachable graphs. For example, ECG is such an unreachable graph. Classical calculus fails in their characterization as derivatives do not exist at the unreachable points. Such unreachable functions can be characterized by fractional calculus as fractional derivatives exist at those unreachable points where classical derivatives do not exist. Definition of fractional derivatives has been proposed by several mathematicians like Grunwald-Letinikov, Riemann-Liouville, Caputo, and Jumarie to develop the theory of fractional calculus. In this paper, we have used Jumarie type fractional derivative and consequently the phase transition (P.T.) which is the difference between left fractional derivative and right fractional derivatives to characterize those points. A comparative study has been done between normal ECG sample and problematic ECG sample (Right Ventricular Hypertrophy) by the help of the above mentioned mathematical tool.

q-bio.OT↗

arXiv2017

Characterization of Left Ventricular Hypertrophy via Fractional Derivatives

In this paper, we have used the concepts of the fractional derivative of rough curves to characterize ECG of LVH patients and compared the results with normal ECGs. In mathematical language, an ECG is a rough curve having Q, R, S points as non-differentiable points where classical derivatives do not exist but fractional derivatives exist. We have calculated both left and right modified Riemann-Liouville fractional derivatives and their differences termed as phase transition at those non-differentiable points of V1, V2, V5, and V6 leads.Investigation shows that phase transition is higher for LVH patients than normal ones. This may be a method of determination of risk factor of LVH patients before doing Echocardiogram.

physics.med-ph↗

arXiv2017

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

In this paper we obtain approximate bound state solutions of $N$-dimensional fractional time independent Schrödinger equation for generalised Mie-type potential, namely $V(r^α)=\frac{A}{r^{2α}}+\frac{B}{r^α}+C$. Here $α(0<α<1)$ acts like a fractional parameter for the space variable $r$. When $α=1$ 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 Jumarie type fractional derivative approach. The solution is expressed via Mittag-Leffler function and fractionally defined confluent hypergeometric function. To ensure the validity of the present work, obtained results are verified with the previous works for different potential parameter configurations, specially for $α=1$. At the end, few numerical calculations for energy eigenvalue and bound states eigenfunctions are furnished for a typical diatomic molecule.

math-ph↗

arXiv2016

A Study of Fractional Schrodinger Equation-composed via Jumarie fractional derivative

One of the motivations for using fractional calculus in physical systems is due to fact that many times, in the space and time variables we are dealing which exhibit coarse-grained phenomena, meaning that infinitesimal quantities cannot be placed arbitrarily to zero-rather they are non-zero with a minimum length. Especially when we are dealing in microscopic to mesoscopic level of systems. Meaning if we denote x the point in space and t as point in time; then the differentials dx (and dt) cannot be taken to limit zero, rather it has spread. A way to take this into account is to use infinitesimal quantities as (\Deltax)^α(and (\Deltat)^α) with 0<α<1, which for very-very small \Deltax (and \Deltat); that is trending towards zero, these 'fractional' differentials are greater that \Deltax (and \Deltat). That is (\Deltax)^α>\Deltax. This way defining the differentials-or rather fractional differentials makes us to use fractional derivatives in the study of dynamic systems. In fractional calculus the fractional order trigonometric functions play important role. The Mittag-Leffler function which plays important role in the field of fractional calculus; and the fractional order trigonometric functions are defined using this Mittag-Leffler function. In this paper we established the fractional order Schrodinger equation-composed via Jumarie fractional derivative; and its solution in terms of Mittag-Leffler function with complex arguments and derive some properties of the fractional Schrodinger equation that are studied for the case of particle in one dimensional infinite potential well.

physics.gen-ph↗

arXiv2016

Analytical Solutions of Classical and Fractional KP-Burger Equation and Coupled KdV equation

Evaluation of analytical solutions of non-linear partial differential equations (both classical and fractional) is a rising subject in Applied Mathematics because its applications in Physical biological and social sciences. In this paper we have used generalized Tanh method to find the exact solution of KP-Burger equation and coupled KdV equation. The fractional Sub-equation method has been used to find the solution of fractional KP-Burger equation and fractional coupled KdV equations. The exact solution obtained by fractional sub-equation method reduces to classical solution when order of fractional derivative tends to one. Finally numerical simulation has done. The numerical simulation justifies that the solutions of two fractional differential equations reduces to shock solution for KP-Burger equation and soliton solution for coupled KdV equations when order of derivative tends to one.

nlin.PS↗

arXiv2015

Solution of System of Linear Fractional Differential Equations with Modified derivative of Jumarie Type

Solution of fractional differential equations is an emerging area of present day research because such equations arise in various applied fields. In this paper we have developed analytical method to solve the system of fractional differential equations in-terms of Mittag-Leffler function and generalized Sine and Cosine functions, where the fractional derivative operator is of Jumarie type. The use of Jumarie type fractional derivative, which is modified Rieman-Liouvellie fractional derivative, eases the solution to such fractional order systems. The use of this type of Jumarie fractional derivative gives a conjugation with classical methods of solution of system of linear integer order differential equations, by usage of Mittag-Leffler and generalized trigonometric functions. The ease of this method and its conjugation to classical method to solve system of linear fractional differential equation is appealing to researchers in fractional dynamic systems. Here after developing the method, the algorithm is applied in physical system of fractional differential equation. The analytical results obtained are then graphically plotted for several examples for system of linear fractional differential equation.

math.CA↗

arXiv2015

Analytical solution with tanh-method and fractional sub-equation method for non-linear partial differential equations and corresponding fractional differential equation composed with Jumarie fractional derivative

The solution of non-linear differential equation, non-linear partial differential equation and non-linear fractional differential equation is current research in Applied Science. Here tanh-method and Fractional Sub-Equation methods are used to solve three non-linear differential equations and the corresponding fractional differential equation. The fractional differential equations here are composed with Jumarie fractional derivative. Both the solution is obtained in analytical traveling wave solution form. We have not come across solutions of these equations reported anywhere earlier.

math.GM↗

arXiv2015

Fractional Weierstrass function by application of Jumarie fractional trigonometric functions and its analysis

The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we define the fractional order Weierstrass function in terms of Jumarie fractional trigonometric functions. The Holder exponent and Box dimension of this function are calculated here. It is established that the Holder exponent and Box dimension of this fractional order Weierstrass function are the same as in the original Weierstrass function, independent of incorporating the fractional trigonometric function. This is new development in generalizing the classical Weierstrass function by usage of fractional trigonometric function and obtain its character and also of fractional derivative of fractional Weierstrass function by Jumarie fractional derivative, and establishing that roughness index are invariant to this generalization.

math.CA↗

arXiv2015

Solutions of Linear Fractional non-Homogeneous Differential Equations with Jumarie Fractional Derivative and Evaluation of Particular Integrals

In this paper we describe a method to solve the linear non-homogeneous fractional differential equations (FDE), composed with Jumarie type Fractional Derivative, and describe this method developed by us, to find out Particular Integrals, for several types of forcing functions. The solutions are obtained in terms of Mittag-Leffler functions, fractional sine and cosine functions. We have used our earlier developed method of finding solution to homogeneous FDE composed via Jumarie fractional derivative, and extended this to non-homogeneous FDE. We have demonstrated these developed methods with few examples of FDE, and also applied in fractional damped forced differential equation. This method proposed by us is useful as it is having conjugation with the classical methods of solving non-homogeneous linear differential equations, and also useful in understanding physical systems described by FDE.

math.CA↗

arXiv2015

Analytic Solution of Linear Fractional Differential Equation with Jumarie Derivative in Term of Mittag-Leffler Function

There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied. Here we develop an algorithm to solve the linear fractional differential equation composed via Jumarie fractional derivative in terms of Mittag-Leffler function; and show its conjugation with ordinary calculus. In these fractional differential equations the one parameter Mittag-Leffler function plays the role similar as exponential function used in ordinary differential equations.

math.CA↗