A Note on an Order Level Inventory Model with Varying Two-Phased Demand and Time-Proportional Deterioration

The main purpose of this paper is to generalize the effect of two-phased demand and variable deterioration within the EOQ (Economic Order Quantity) framework. The rate of deterioration is a linear function of time. The two-phased demand function states the constant function for a certain period and the quadratic function of time for the rest part of the cycle time. No shortages as well as partial backlogging are allowed to occur. The mathematical expressions are derived for determining the optimal cycle time, order quantity and total cost function. An easy-to-use working procedure is provided to calculate the above quantities. A couple of numerical examples are cited to explain the theoretical results and sensitivity analysis of some selected examples is carried out.

Optimal Policy for EOQ Model with Two Level of Trade Credits in One Replenishment Cycle

In general, a supplier/retailer frequently offer trade credit to stimulate their respective sales. The main purpose of this paper is to investigate the optimal supplier/retailer’s replenishment decisions under two levels of trade credit policy within the economic order quantity (EOQ) framework. This paper deals with the supplier/retailer’s inventory replenishment problem under two levels of trade credit in one replenishment cycle. A different approach of two levels of trade credit is used, which give more freedom to the supplier/retailer in business. In addition, the easy-to-use procedure is developed to efficiently find the optimal cycle time for the retailer under minimizing annual total relevant cost. Finally, a numerical example is given to illustrate these results.

A robust computational approach for Zakharov-Kuznetsov equations of ion-acoustic waves in a magnetized plasma via the Shehu transform

The application of the q-homotopy analysis Shehu transform method(q-HAShTM)to discover the esti-mated solution of fractional Zakharov-Kuznetsov equations is investigated in this study.In the presence of a uniform magnetic field,the Zakharov-Kuznetsov equations regulate the behaviour of nonlinear acoustic waves in a plasma containing cold ions and hot isothermal electrons.The q-HAShTM is a stable analytical method that combines homotopy analysis and the Shehu transform.This q-homotopy investigation Shehu transform is a constructive method that leads to the Zakharov-Kuznetsov equations,which regulate the propagation of nonlinear ion-acoustic waves in a plasma.It is a more semi-analytical method for adjust-ing and controlling the convergence region of the series solution and overcoming some of the homotopy analysis method’s limitations.

Solution for generalized fuzzy time-fractional Fisher’s equation using a robust fuzzy analytical approach

This work focuses on designing and analyzing a double parametric fuzzy Homotopy analysis approach with Shehu transform for the non-linear fuzzy time-fractional generalized Fisher’s equation(FTFGFE).A triangular fuzzy number is used to describe the Caputo fractional derivative(CFD)of order(0,1)that appears in the modeling problem.A novel double parametric form-based Homotopy analysis approach with its convergence analysis is introduced to examine the fuzzy velocities profiles at different spatial positions with crisp and fuzzy conditions.Additional examples are offered to demonstrate the method’s efficacy and viability.The resulting results are compared to otherα=1 results to validate the obtained results and to test the efficiency of the proposed method.The errors approximations are provided to support the suggested computing efficiency of the analytical method.

Fractional order reaction diffusion of calcium regulating NFAT production in T Lymphocyte

Ca^(2+)signals have a crucial role in the immune system for cell functions such as proliferation,differentiation,apoptosis and gene transcription as well as the activation of Nuclear factor of activated T Cell(NFAT)which modulates the immune response of the cells.In this study,a fractional order spatiotemporal calcium dynamics model is formulated using the reaction-diffusion equation incorporating parameters like buffers,source influx,Jsscyt and J_(PMCA).Grinwald estimation is employed to obtain the solution and stability analysis has been performed.The analysis of numerical results provides novel insights about the role of Brownian motion,super diffusion,source influx,buffers,etc.,in the regulation of calcium and NFAT concentration levels in T cell and the conditions which might lead to disordered immune responses causing diseases such as HINI,HIV and HBV.

A robust fuzzy-fractional approach for the atmospheric internal wave model

The study of internal atmospheric waves,also known as gravity waves,which are detectable inside the fluid rather than at the fluid surface,is presented in this work.We have used the time-fractional and fuzzy-fractional techniques to solve the differential equation system representing the atmospheric inter-nal waves model.The q-Homotopy analysis Shehu transform technique(q-HAShTM)is used to solve the model.The method helps find convergent solutions since it helps solve nonlinearity,and the fractional derivative can be easily computed using the Shehu transform.Finally,the obtained solution is compared for the particular case ofα=1 with the HAM solution to explain the method’s accuracy.

Generalized Multiobjective Symmetric Duality under Second-Order(F, α, ρ, d)-Convexity

In this paper, we first formulate a second-order multiobjective symmetric primal-dual pair over arbitrary cones by introducing two different functions f ： R^n × R^m → Rk and g ： R^n × R^m → R^l in each k-objectives as well as l-constraints. Further, appropriate duality relations are established under second-order（F, α, ρ, d）-convexity assumptions. A nontrivial example which is second-order（F, α, ρ, d）-convex but not secondorder convex/F-convex is also illustrated. Moreover, a second-order minimax mixed integer dual programs is formulated and a duality theorem is established using second-order（F, α, ρ, d）-convexity assumptions. A self duality theorem is also obtained by assuming the functions involved to be skew-symmetric.

An efficient technique for solving fractional-order diffusion equations arising in oil pollution

In this article,non-linear time-fractional diffusion equations are considered to describe oil pollution in the water.The latest technique,fractional reduced differential transform method(FRDTM),is used to ac-quire approximate solutions of the time fractional-order diffusion equation and two cases of Allen-Cahn equations.The acquired results are collated with the exact solutions and other results from literature for integer-orderα,which reveal that the proposed method is effective.Hence,FRDTM can be employed to obtain solutions for different types of nonlinear fractional-order IVPs arising in engineering and science.