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

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International Journal of Biomathematics 2019年第5期12卷 241-261页

作者： Ved Prakash Dubey Rajnesh Kumar Devendra Kumar faculty of mathematical and statistical sciences shri Ramswaroop Memorial university Lucknow-Deva Road Uttar Pradesh-225003India Department of Mathematics University of Rajasthan Jaipur-302004RajasthanIndia

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 *** this paper,an effective and powerful mathematical technique,*** homotopy analysis transform method (FHATM),is employed to get the numerical solutions of biochemical reaction model with time fractional *** adopted scheme is the beautiful copulation of homotopy analysis technique and Laplace transform *** paper shows that the adopted scheme is quite easy as well as computationally attractive in the context of a solution *** Caputo-type fractional derivatives are considered in the present *** 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 *** time fractional biochemical reaction model with respect to stability analysis for various values of fractional order q is also *** 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.

关键词： Biochemical reaction model FHATM Laplace transform homotopy stability analysis fractional order

Studying the efficacy of isolation as a control strategy and elimination of tuberculosis in India:A mathematical model

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Infectious Disease Modelling 2023年第2期8卷 458-470页

作者： Archana Singh Bhadauria Hom Nath Dhungana Vinay Verma Stephen Woodcock Tapan Rai Department of Mathematics and Statistics Deen Dayal Upadhyaya Gorakhpur UniversityIndia School of mathematical and Physical sciences University of Technology SydneyAustralia faculty of mathematical and statistical sciences Institute of Natural Sciences and HumanitiesShri Ramswaroop Memorial UniversityUttar PradeshIndia

India has the highest burden of both tuberculosis(TB)and multidrug-resistant TB(MDRTB)based on the WHO Global TB Report *** the available data suggest that the total TB incidence has declined,the absolute number of new cases is still *** number of reported TB cases in India in 2018 was 2.2 million,which was 1.5 million in *** 47%increment in TB case notification in India within a decade shows a persistent public health *** contributes about 22%of the World's TB *** National Strategic Plan 2017e2025,sets out the government plans to eliminate TB by ***,the milestone seems unrealistic to achieve the TB eradication goal by *** developed a five-dimensional mathematical model to understand the TB dynamics in India and investigate the possibility of the earliest TB eradication time *** model stratifies the entire TB class into three different classes as drug-sensitive(DS),MDR,and isolated *** effective reproduction number,equilibrium points,and stability analysis of the model were carried *** model predicts the total estimated cases of DS-TB and MDR-TB from 2018 to 2035 through numerical simulation and suggests that TB may be eliminated by 2035 in India if the treatment success rate could be achieved to 95%,by contact tracing and isolating at least 50%of MDR-TB.

关键词： Multi-drug resistant Drug-sensitive Isolation Reproduction number mathematical modelling

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

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Communications in Theoretical Physics 2023年第12期75卷 12-18页

作者： Jagdev Singh Hassan Kamil Jassim Devendra Kumar Ved Prakash Dubey Department of Mathematics JECRC UniversityJaipurRajasthanIndia Department of Mathematics Kyung Hee University26 Kyungheedae-roDongdaemun-guSeoul02447Republic of Korea Department of Computer Science and Mathematics Lebanese American UniversityBeirutLebanon Department of Mathematics Faculty of Education for Pure SciencesUniversity of Thi-QarNasiriyahIraq Department of Mathematics University of RajasthanJaipur-302004RajasthanIndia faculty of mathematical and statistical sciences Shri Ramswaroop Memorial UniversityBarabanki-225003Uttar PradeshIndia

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

关键词： poisson equation local fractional natural transform adomian decomposition method local fractional derivative electrostatics fractal media

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

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Journal of Ocean Engineering and Science 2021年第1期6卷 30-39页

作者： Ved Prakash Dubey Rajnesh Kumar Jagdev Singh Devendra Kumar faculty of mathematical and statistical sciences Shri Ramswaroop Memorial UniversityLucknow-Deva RoadUttar Pradesh-225003India Department of Applied Science and Humanities Government Engineering CollegeNawadaDepartment of Science and TechnologyBihar-805122India Department of Mathematics JECRC UniversityJaipur-303905RajasthanIndia Department of Mathematics University of RajasthanJaipur-302004RajasthanIndia

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)*** present study considers the Caputo fractional *** fractional order modified DP model is very important and plays a great role in study of ocean engineering and *** 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 *** 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 *** 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.

关键词： Fractional Degasperis-Procesi equation Nonlinear dispersive waves Analytical solution q-homotopy analysis method Sumudu transform