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1

Study of memory effect in an economic order quantity model with quadratic type demand rate

Pakhira R., Ghosh U., Sarkar S.

Computational Methods in Science and Technology

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2019

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Vol. 25, No. 2

71--80

EN

The study of memory effect in an economic order quantity model has a great impact on the inventory system. Although business policy almost depends on the past experiences of the system, usually the classical inventory model does not include the past experience or memory effect, i.e. one important part of the system is ignored. Our purpose is to include memory or past experience in the inventory model. The purpose of this paper is to incorporate the existence of dynamic memory in an inventory model with shortage via fractional calculus. To derive the memory dependent inventory model associated with inventory holding cost, shortage cost has been developed. Analytical solution of the proposed inventory model has been solved via primal geometric programming method. Numerically long memory effect or short memory effect of the inventory system has been established. In this paper, an effort has also been made to compare the memory effect on the minimized total average cost and the optimal ordering interval using different numerical examples.

2

Qualitative Analysis of Both Hyperbolic and Non-hyperbolic Equilibria of a SIRS Model with Logistic Growth Rate of Susceptibles and Inhibitory Effect in the Infection

Ghosh J. K., Ghosh U., Sarkar S.

Computational Methods in Science and Technology

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2018

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Vol. 24, No. 4

285--300

EN

This paper describes a SIRS model with the logistic growth rate of susceptible class. The effect of an inhibitory factor in the infection is also taken into consideration. We have analysed local as well as global stabilities of the equilibrium points (both hyperbolic and non-hyperbolic) of the system and investigated the Transcritical bifurcation at the disease free equilibrium point with respect to the inhibitory factor. The occurrence of Hopf bifurcation of the system is examined and it was observed that this Hopf bifurcation is either supercritical or subcritical depending on parameters. Some numerical simulations are carried out for the validity of theoretical results.

3

Global Stability Analysis of Logistically Grown SIR Model with Loss of Immunity, Inhibitory Effect, Crowding Effect and its Protection Measure

Ghosh U., Sarkar S.

Computational Methods in Science and Technology

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2018

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Vol. 24, No. 2

125--141

EN

In this paper we have considered an SIR model with logistically grown susceptible in which the rate of incidence is directly affected by the inhibitory factors of both susceptible and infected populations and the protection measure for the infected class. Permanence of the solutions, global stability and bifurcation analysis in the neighborhood of equilibrium points has been investigated here. The Center manifold theory is used to find the direction of bifurcations. Finally numerical simulation is carried out to justify the theoretical findings.

4

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

Ghosh U., Sarkar S., Das S.

Computational Methods in Science and Technology

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2016

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Vol. 22, No. 3

143--152

EN

Development of new analytical and numerical methods and their applications for solving non-linear partial differential equations (both classical and fractional) is a rising field of Applied Mathematical research because of its applications in Physical, Biological and Social Sciences. In this paper we have used a 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 the fractional sub-equation method reduces to classical solution when the order of fractional derivative tends to one. Finally numerical simulation has been done. The numerical simulation justifies that the solutions of two fractional differential equations reduce to shock solution for KP-Burger equation and soliton solution for coupled KdV equations when the order of derivative tends to one.