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Analytical and Numerical Solutions of Riesz Space Fractional Advection-Dispersion Equations with Delay

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Computer Modeling in Engineering & Sciences 2019年第10期121卷 249-272页

作者： Mahdi Saedshoar Heris Mohammad Javidi bashir ahmad Department of Applied Mathematics University of TabrizTabrizIran Nonlinear Analysis and Applied Mathematics(NAAM)Research Group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia.

In this paper,we propose numerical methods for the Riesz space fractional advection-dispersion equations with delay(RFADED).We utilize the fractional backward differential formulas method of second order(FBDF2)and weighted shifted Grünwald difference(WSGD)operators to approximate the Riesz fractional derivative and present the finite difference method for the ***,the FBDF2 and the shifted Grünwald methods are ***,based on the FBDF2 method and the WSGD operators,the finite difference method is applied to the *** also show that our numerical schemes are conditionally stable and convergent with the accuracy of O(+h2)and O(2+h2)*** we find the analytical solution for RFDED in terms Mittag-Leffler type ***,some numerical examples are given to show the efficacy of the numerical methods and the results are found to be in complete agreement with the analytical solution.

关键词： Riesz fractional derivative shifted Grünwald difference operators fractional advection-dispersion equation delay differential equations FBDF method

Peristaltic flow in an asymmetric channel with convective boundary conditions and Joule heating

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Journal of Central South University 2014年第4期21卷 1411-1416页

作者： Abbasi Fahad Munir Hayat Tasawar ahmad bashir Department of Mathematics Quaid-I-Azam University Nonlinear Analysis and Applied Mathematics (NAAM) Research Group Faculty of ScienceKing Abdulaziz University

The peristaltic transport of viscous fluid in an asymmetric channel is concentrated. The channel walls exhibit convective boundary conditions. Both cases of hydrodynamic and magnetohydrodynamic(MHD) fluids are considered. Mathematical analysis has been presented in a wave frame of reference. The resulting problems are non-dimensionalized. Long wavelength and low Reynolds number approximations are employed. Joule heating effect on the thermal equation is retained. Analytic solutions for stream function and temperature are constructed. Numerical integration is carried out for pressure rise per wavelength. Effects of influential flow parameters have been pointed out through graphs.

关键词： peristaltic flow convective conditions Joule heating

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

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Acta Mathematica Scientia 2011年第6期31卷 2122-2130页

作者： bashir ahmad Juan J. Nieto Ahmed Alsaedi Department of Mathematics Faculty of ScienceKing Abdulaziz University Departamento de Anlisis Matemtico Facultad de MatemticasUniversidad de Santiago de Compostela

In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.

关键词： fractional differential equations non-separated integral boundary conditions contraction principle Krasnoselskii's fixed point theorem LeraySchauder degree

A NONLOCAL HYBRID BOUNDARY VALUE PROBLEM OF CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 2016年第6期36卷 1631-1640页

作者： bashir ahmad Sotiris K.NTOUYAS Jessada TARIBOON Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group Department of MathematicsFaculty of ScienceKing Abdulaziz University Department of Mathematics University of Ioannina Nonlinear Dynamic Analysis Research Center Department of MathematicsFaculty of Applied ScienceKing Mongkut’s University of Technology North Bangkok

In this paper, we discuss the existence of solutions for a nonlocal hybrid boundary value problem of Caputo fractional integro-differential equations. Our main result is based on a hybrid fixed point theorem for a sum... 详细信息

关键词： Caputo fractional derivative integral hybrid fixed point theorem

Optimal Control Model for the Transmission of Novel COVID-19

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Computers, Materials & Continua 2021年第3期66卷 3089-3106页

作者： Isa Abdullahi Baba bashir ahmad Nasidi Dumitru Baleanu Department of Mathematical Sciences Bayero University KanoNigeria Department of Mathematics Cankaya UniversityAnkara06530Turkey Institute of Space Sciences BucharestRomania Department of Medical Research China Medical University HospitalTaichungTaiwan

As the corona virus(COVID-19)pandemic ravages socio-economic activities in addition to devastating infectious and fatal consequences,optimal control strategy is an effectivemeasure that neutralizes the scourge to its lowest *** this paper,we present a mathematical model for the dynamics of COVID-19,and then we added an optimal control function to the model in order to effectively control the *** incorporate three main control efforts(isolation,quarantine and hospitalization)into the model aimed at controlling the spread of the *** efforts are further subdivided into five functions;u1(t)(isolation of the susceptible communities),u2(t)(contact track measure by which susceptible individuals with contact history are quarantined),u3(t)(contact track measure by which infected individualsare quarantined),u4(t)(control effort of hospitalizing the infected I1)and u5(t)(control effort of hospitalizing the infected I2).We establish the existence of the optimal control and also its characterization by applying Pontryaging maximum *** disease free equilibrium solution(DFE)is found to be locally asymptotically stable and subsequently we used it to obtain the key parameter;basic reproduction *** constructed Lyapunov function to which global stability of the solutions is *** simulations show how adopting the available control measures optimally,will drastically reduce the infectious populations.

关键词： COVID-19 optimal control Pontryaging maximum principle mathematical model existence of control stability analysis

DYNAMICS OF A HEPATITIS B MODEL WITH SATURATED INCIDENCE

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Acta Mathematica Scientia 2018年第6期38卷 1731-1750页

作者： Liya LIU Daqing JIANG Tasawar HAYAT bashir ahmad. School of Petroleum Engineering China University of Petroleum Qingdao 266580 China College of Science China University of Petroleum Qingdao 266580 China Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group King Abdulaziz University Jeddah Saudi Arabia Department of Mathematics Quaid-I-Azam University45320 Islamabad 44000 Pakistan

In this article, we present a hepatitis B epidemic model with saturated *** dynamic behaviors of the deterministic and stochastic system are studied. To thisend, we first establish the local and global stability conditions of the equilibrium of thedeterministic model. Second, by constructing suitable stochastic Lyapunov functions, thesufficient conditions for the existence of ergodic stationary distribution as well as extinctionof hepatitis B are obtained.

关键词： hepatitis B model Lyapunov function stability stationary distribution ex-tinction

A predictor-corrector scheme for solving nonlinear fractional differential equations with uniform and nonuniform meshes

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International Journal of Modeling, Simulation, and Scientific Computing 2019年第5期10卷 108-142页

作者： Mohammad Javidi Mahdi Saedshoar Heris bashir ahmad Faculty of Mathematical Sciences University of Tabriz TabrizIran Nonlinear Analysis and Applied Mathematics Research Group(NAAM)King Abdulaziz University P.O.Box 80203 Jeddah 21589Saudi Arabia

In this paper,we develop two algorithms for solving linear and nonlinear fractional differential equations involving Caputo *** designing new predictor–corrector(PC)schemes,we select the mesh points based on the two equal-height and equal-area ***,the error bounds of PC schemes with uniform and equidistributing meshes are ***,examples are constructed for illustrating the obtained PC schemes with uniform and equidistributing meshes.A comparative study is also presented.

关键词： meshes fractional uniform

ON A COUPLED INTEGRO-DIFFERENTIAL SYSTEM INVOLVING MIXED FRACTIONAL DERIVATIVES AND INTEGRALS OF DIFFERENT ORDERS

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Acta Mathematica Scientia 2021年第4期41卷 1366-1384页

作者： bashir ahmad Ravi P.AGARWAL Abrar BROOM Ahmed ALSAEDI Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityP.O.Box 80203Jeddah 21589Saudi Arabia Department of Mathematics Texas A&M UniversityKingsvilleTexas 78363-8202USA

By applying the standard fixed point theorems,we prove the existence and uniqueness results for a system of coupled differential equations involving both left Caputo and right Riemann-Liouville fractional derivatives and mixed fractional integrals,supplemented with nonlocal coupled fractional integral boundary *** example is also constructed for the illustration of the obtained results.

关键词： Fractional differential equations Caputo and Riemann-Liouville fractional derivatives systems existence fixed point theorems

Impact of Transformational Leadership on Construction Projects in Pakistan

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Impact of Transformational Leadership on Construction Projec...

作者： bashir ahmad 山东大学

学位级别：硕士

领导领域因其涉及不同工作成果的范围而吸引了更多的研究。这项研究的目的是找出在项目沟通的中介作用下,变革型领导对项目绩效的影响。这项研究由一个自变量(转型领导力),一个因变量(项目绩效)和一个中介变量(项目沟通)组成。通过结构... 详细信息

领导领域因其涉及不同工作成果的范围而吸引了更多的研究。这项研究的目的是找出在项目沟通的中介作用下,变革型领导对项目绩效的影响。这项研究由一个自变量(转型领导力),一个因变量(项目绩效)和一个中介变量(项目沟通)组成。通过结构化的问卷调查,从200名员工从巴基斯坦开伯尔-普赫图赫瓦省开展的建设项目中收集了数据。描述性统计数据,α可靠性,每个变量的平均值通过SPSS找到。此外,使用相关和回归分析来找到当前研究的假设和变量之间的关联。这项研究的发现发现了有意义的关联和影响。在哪里,所有假设都得到支持和接受。领导力是组织通过激励员工来实现其目标的关键角色。领导者包括管理人员和主管,他们应专注于变革型的领导方式,以帮助在预定的时限,成本和范围内实现项目目标,从而通过及时的基础沟通避免不确定性和模棱两可。这项研究考察了变革型领导与项目绩效之间沟通的影响,沟通为提高生产力提供了参考。经理,领导和主管应以沟通的方式提高项目绩效。

关键词：变革型领导项目沟通项目绩效