Fractal dynamics and computational analysis of local fractional Poisson equations arising in electrostatics

In this paper,the local fractional natural decomposition method(LFNDM)is used for solving a local fractional Poisson equation.The local fractional Poisson equation plays a significant role in the study of a potential field due to a fixed electric charge or mass density distribution.Numerical examples with computer simulations are presented in this paper.The obtained results show that LFNDM is effective and convenient for application.

近20年印度北阿坎德邦奈尼塔尔地区农业面积变化

本研究对印度北阿坎德邦奈尼塔尔地区的农业用地进行了时间序列分析。该研究基于Landsat5,Landsat7and Landsat8卫星图像数据,使用随机森林分类器对该区域近21年(2000–2021年)的农业和非农业土地进行分类。陆地卫星图像使用谷歌地球引擎(GEE)平台进行处理,随机森林分类器的选择则是基于随机森林(RF)、支持向量机(SVM)和分类与回归树(CART)之间的比较分析。对总体准确度、用户准确度、生产者准确度和Kappa系数进行了评估,以确定研究区域的最佳分类器。结果表明,2021年RF、SVM和CART的总体准确率分别为96.38%、94.44%和91.94%;类似地,RF、SVM和CART的Kappa系数分别为0.96、0.89和0.81。陆地卫星在农业和非农业地区的分类图像显示,该区域在21年间(2000–2021年)农业用地减少了4.71%。该研究还表明,过去4年(即2018–2021年)该区域农业面积下降幅度最大。本研究对于发展中国家了解农用地变化并采取适当措施以保护该地区的动植物非常重要。

Approximate analytical solution of fractional order biochemical reaction model and its stability analysis

Approximate analytical solution of the system of coupled nonlinear Ordinary Differential Equations (ODEs) of a biochemical reaction model is much relevant due to its practical significance to biochemists.In this paper,an effective and powerful mathematical technique,viz.fractional homotopy analysis transform method (FHATM),is employed to get the numerical solutions of biochemical reaction model with time fractional derivatives.The adopted scheme is the beautiful copulation of homotopy analysis technique and Laplace transform algorithm.This paper shows that the adopted scheme is quite easy as well as computationally attractive in the context of a solution procedure.The Caputo-type fractional derivatives are considered in the present paper.Approximate results of the probability density functions of the time fractional biochemical reaction model are computed for miscellaneous fractional Brownian motions as well as for classical motion and are presented graphically.The time fractional biochemical reaction model with respect to stability analysis for various values of fractional order q is also analyzed.In the context of stability discussion,we have used the fractional Routh-Hurwitz stability criterion to establish the local stability of the biochemical reaction model of fractional order.

Numerical solution of time-fractional three-species food chain model arising in the realm of mathematical ecology

T'his research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives.The offered technique is a fantastic blend of homotopy analysis method(HAM)and Laplace transform(LT)operator and has been used fruitfully in the numerical computation of various fractional differential equations(FDEs).This paper involves the fractional derivatives of Caputo style.The numerical solutions of this selected fractional-order food chain model are evaluated by making use of the associated initial conditions.It is revealed by the adopting procedure that the more desirable estimation of the solution can be easily acquired through the calculation of some number of iteration terms only-a fact which authenticates the easiness and soundness of the suggested hybrid scherne.The variations of fractional order of time derivative on the solutions for different specific cases have been depicted through graphical presentations.The outcomes demonstrated through the graphs expound that the adopted scheme is very fantastic and accurate.

An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves

In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)equation.The present study considers the Caputo fractional derivative.The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science.The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter h and the asymptotic parameterρ(≥1)to handle mainly the differential equations of nonlinear nature.The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution.The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameterβ.