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Fractional Analysis of Viscous Fluid Flow with Heat and Mass Transfer Over a Flexible Rotating Disk

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Computer Modeling in Engineering & Sciences 2020年第4期123卷 377-400页

作者： muhammad Shuaib muhammad Bilal muhammad altaf khan Sharaf J.Malebary Department of Mathematics City University of Science and Information TechnologyPeshawarPakistan Institute for Groundwater Studies Faculty of Natural and Agricultural SciencesUniversity of the Free StateBloemfonteinSouth Africa Department of Information Technology Faculty of Computing and Information TechnologyKing Abdulaziz UniversityRabighSaudia Arabia

An unsteady viscous fluid flow with Dufour and Soret effect,which results in heat and mass transfer due to upward and downward motion of flexible rotating disk,has been *** upward or downward motion of non rotating disk results in two dimensional flow,while the vertical action and rotation of the disk results in three dimensional *** using an appropriate transformation the governing equations are transformed into the system of ordinary differential *** system of ordinary differential equations is further converted into first order differential equation by selecting suitable ***,we generalize the model by using the Caputo *** numerical result for the fractional model is presented and validated with Runge Kutta order 4 method for classical *** compared results are presented in Table and *** is concluded that the fractional model is more realistic than that of classical one,because it simulates the fluid behavior at each fractional value rather than the integral values.

关键词： Caputo derivatives similarity transformation RK4 soret effect Dufour effect

Mathematical modeling approach to the transmission dynamics of pine wilt disease with saturated incidence rate

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International Journal of Biomathematics 2018年第3期11卷 77-96页

作者： muhammad altaf khan Kamil Shaht Yasir khan Saeed Islam Department of Mathematics City University of Science and Information Technology Peshawar Khyber Pakhtunkhwa 25000 Pakistan Department of Mathematics University of Haft A1 Batin Hafr Al Batin 31991 Saudi Arabia Department of Mathematics Abdul Wall khan University Mardan Khyber Pakhtunkhwa 23200 Pakistan

The present paper investigates the dynamics of pine wilt disease with saturated incidence rate. The proposed model is stable both locally and globally. The local stability of the disease-free equilibrium is determined by the basic reproduction R0. The disease-free equilibrium is stable locally and globally whenever R0〈 1. If R0 〉 1, then the endemic state is stable both locally and globally. Further, a brief discussion with conclusion on the numerical results of the proposed model is presented.

关键词： SEIVRS mathematical model pine wilt disease stability analysis numerical simulation.

Dynamical system of a SEIQV epidemic model with nonlinear generalized incidence rate arising in biology

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International Journal of Biomathematics 2017年第7期10卷 107-125页

作者： muhammad altaf khan Yasir khan Taj Wali khan Saeed Islam Department of Mathematics Abdul Wali khan University Mardan Khyber Pakhtunkhwa Pakistan Department of Mathematics University of Haft Al-Batin Haft Al-Batin 31991 Saudi Arabia

In this paper, a dynamical system of a SEIQV mathematical model with nonlinear generalized incidence arising in biology is investigated. The stability of the disease-free and endemic equilibrium is discussed. The basic reproduction number of the model is obtained. We found that the disease-free and endemic equilibrium is stable locally as well as globally asymptotically stable. For R0〈1, the disease-free equilibrium is stable both locally and globally and for R0〉1, the endemic equilibrium is stable globally asymptotically. Finally, some numerical results are presented.

关键词： Epidemic model SEIQV model vaccination global stability numerical solution.

Global stability of SEIVR epidemic model with generalized incidence and preventive vaccination

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International Journal of Biomathematics 2015年第6期8卷 203-221页

作者： muhammad altaf khan Yasir khan Qaiser Badshah Saeed Islam Department of Mathematics Abdul Wali Khan University Mardan Khyber Pakhtunkhwa 23200 Pakistan Department of Mathematics University of Haft Al-Batin Haft Al-Batin 31991 Saudi Arabia Department of Mathematics Abdul Wall Khan University Mardan Khyber Pakhtunkhwa 23200 Pakistan

In this paper, an SEIVR epidemic model with generalized incidence and preventive vaccination is considered. First, we formulate the model and obtain its basic properties. Then, we find the equilibrium points of the model, the disease-free and the endemic equilibrium. The stability of disease-free and endemic equilibrium is associated with the basic reproduction number R0. If the basic reproduction number R0〈 1, the disease- free equilibrium is locally as well as globally asymptotically stable. Moreover, if the basic reproduction number R0 〉 1, the disease is uniformly persistent and the unique endemic equilibrium of the system is locally as well as globally asymptotically stable under certain conditions. Finally, the numerical results justify the analytical results.

关键词： SEIVR reproduction number global stability numerical results.

Global stability and vaccination of an SEIVR epidemic model with saturated incidence rate

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International Journal of Biomathematics 2016年第5期9卷 59-83页

作者： muhammad altaf khan Yasir khan Sehra khant Saeed Islam Department of Mathematics Abdul Wall khan University Mardan Khyber Pakhtunkhwa 23200 Pakistan Department of Mathematics University of Haft Al-Batin Hafr Al-Batin 31991 Saudi Arabia Department of Mathematics Abdul Wali khan University Mardan Khyber Pakhtunkhwa 23200 Pakistan

This study considers SEIVR epidemic model with generalized nonlinear saturated inci- dence rate in the host population horizontally to estimate local and global equilibriums. By using the Rout^Hurwitz criteria, it is shown that if the basic reproduction number R0 〈 1, the disease-free equilibrium is locally asymptotically stable. When the basic reproduction number exceeds the unity, then the endemic equilibrium exists and is stable locally asymptotically. The system is globally asymptotically stable about the disease-free equilibrium if R0 〈 1. The geometric approach is used to present the global stability of the endemic equilibrium. For R0〉 1, the endemic equilibrium is stable globally asymptotically. Finally, the numerical results are presented to justify the mathematical results.

关键词： Epidemic model reproduction number vaccination global stability Routh- Hurwitz criteria numerical solution.

A Discrete Model of TB Dynamics in Khyber Pakhtunkhwa-Pakistan

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Computer Modeling in Engineering & Sciences 2020年第5期123卷 777-795页

作者： muhammad altaf khan khanadan khan Mohammad A.Safi Mahmoud H.DarAssi Faculty of Natural and Agricultural Sciences University of the Free StateBloemfonteinSouth Africa Department of Mathematics City University of Science and Information TechnologyPeshawarPakistan Department of Mathematics The Hashemite universityZarqaJordan Department of Basic Sciences Princess Sumaya University for TechnologyAmmanJordan

The present paper investigates the theoretical analysis of the tuberculosis(TB)model in the discrete-time *** model is parameterized by the TB infection cases in the Pakistani province of Khyber Pakhtunkhwa between 2002 and *** model is parameterized and the basic reproduction number is obtained and it is found R_(0)=1:*** stability analysis for the model is presented and it is shown that the discrete-time tuberculosis model is stable at the disease-free equilibrium whenever R_(0)1.A discrete fractional model in the sense of Caputo derivative is *** numerical results of the model with various parameters and their effect on the model are presented.A comparison of discrete-time method with continuous-time model is presented graphically.A discrete fractional approach is compared with the existing method in literature and some reasonable results are ***,a summary of results and conclusion are presented.

关键词： Discrete TB model real data equilibria Lyapunov stability Caputo derivative

Modeling and scientific computing for the transmission dynamics of Avian influenza with half-saturated incidence

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International Journal of Modeling, Simulation, and Scientific Computing 2020年第4期11卷 1-31页

作者： muhammad altaf khan Saif Ullah Yasir khan muhammad Farhan Informetrics Research Group Ton Duc Thang University Ho Chi Minh CityVietnam Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh CityVietnam Department of Mathematics University of PeshawarPakistan Department of Mathematics University of Hafr Al-Batin Hafr Al-Batin 31991Saudi Arabia Department of Mathematics Abdul Wali Khan University Mardan 23200Pakistan

This paper presents the mathematical analysis of the dynamical system for avian *** proposed model considers a nonlinear dynamical model of birds and *** half-saturated incidence rate is used for the transmission of avian influenza *** mathematical results are presented for the proposed *** local and global dynamics of each model are presented and proven that when R01,then the endemic equilibrium is stable both locally and *** numerical results obtained for the proposed model shows that influenza could be eliminated from the community if the threshold is not greater than unity.

关键词： Avian influenza half-saturated incidence rate scientific computing stability analysis numerical results.

Optimal Campaign in Leptospirosis Epidemic by Multiple Control Variables

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Applied Mathematics 2012年第11期3卷 1655-1663页

作者： muhammad altaf khan Gul Zaman Saeed Islam muhammad Ikhlaq Chohan Department of Business Administration and Accounting Buraimi University College Al-Buraimi Oman Department of Mathematics Abdul Wali Khan University Mardan Pakistan Department of Mathematics University of Malakand Chakdara Lower Dir District of Khyber Pakhtunkhwa Pakistan

In this paper, we consider a leptospirosis epidemic model to implement optimal campaign by using multiple control variables. First, we show the existence of the control problem. Then we derive the conditions under which it is optimal to eradicate the leptospirosis infection and examine the impact of a possible educatioal/vaccinaction campaign using Pontryagin’s Maximum Principle. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method. The results obtained from the numerical simulations of the model show that a possible educational/vaccinaction combined with effective treatment regime would reduce the spread of the leptospirosis infection appreciably.

关键词： Mathematical Model Optimal Control Pontryagin’s Maximum Principle Numerical Results

Depositional and Bio-Sequence Stratigraphic Framework of Late Cretaceous Kawagarh Formation,Kala-Chitta Range,Pakistan:Equivalent of Gurpi Formation(Iran)

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Journal of Earth Science 2024年第2期35卷 332-348页

作者： muhammad Awais Bilal Wadood muhammad Ishaq muhammad Bilal Zeeshan Zafar Nasar khan Aminullah khan Department of Geology University of SwabiAnbar-SwabiKhyber PakhtunkhwaSwabi23561Pakistan Department of Earth Environmental and Resources SciencesUniversity of Naples FedericoⅡNaples80126Italy State Key Laboratory of Continental Dynamics Department of GeologyNorthwest UniversityXi’an710069China National Centre of Excellence in Geology University of PeshawarPeshawarKhyber Pakhtunkhwa25130Pakistan Department of Geological Engineering School of Earth Sciences and EngineeringXi’an Shiyou UniversityXi’an610500China Department of Petroleum Geology and Engineering School of Earth ResourcesChina University of GeosciencesWuhan430074China Department of Geology University of MalakandDir Lower18800ChakdaraPakistan Department of Earth and Environmental Sciences KU LeuvenLeuven3001Belgium

The present study is focused on evaluation of deep marine pelagic sediments of Late Cretaceous Kawagarh Formation of Kala-Chitta Range in the context of microfacies analysis,paleoenvironmental interpretation,planktonic foraminiferal biostratigraphy,sequence stratigraphy and diversification of species.A total of thirty three rock samples were collected from the measured *** microfacies are interpreted,namely planktonic foraminifera wackestone,planktonic foraminifera mudstone and sandy mudstone indicating low energy depositional environment i.e.,outer *** biostratigraphic studies show plentiful planktonic foraminifera species of Globotruncana,Heterohelix and ***,no association of benthic or siliceous organisms was *** the basis of available species assemblage,a single local planktonic foraminifera biozone i.e.,Globotruncana-Heterohelix-Globotruncanita Assemblage Biozone is *** biozone information is combined with published literature and Lower Santonian to Middle Maastrichtian age has been assigned to the Kawagarh *** trend of species occurrences evinces that species number decreases over time with pulsated rise in the Kawagarh *** Kawagarh Formation carbonates show an overall Transgressive Systems Tract(TST).The Kawagarh Formation of Pakistan evinces analogous characteristics to that of the Late Cretaceous Gurpi Formation of Iran based on the geologic age,outcrop lithology,microfacies,planktonic foraminiferal assemblages,depositional setting and sequence stratigraphy.

关键词： depositional fabric biostratigraphy sequence stratigraphy Late Cretaceous Kawagarh Formation Pakistan Gurpi Formation Iran