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Acta Mathematica Scientia 2013年第3期33卷 758-772页

作者： dimplekumar N. CHALISHAJAR K. KARTHIKEYAN Department of Mathematics and Computer Science Virginia Military Institute (VMI) 417 Mallory HallLexington VA 24450 USA Department of Mathematics KSR College of TechnologyTiruchengode-637 215 Tamilnadu India

We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ （n-1, n） in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder＇s inequality, a suitable singular Cronwall＇s inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.

关键词： Boundary value problems fractional order integro-differential equations bound-ary value problems existence and uniqueness singular gronwall inequality fixed point theorem

On Applications of Generalized Functions in the Discontinuous Beam Bending Differential Equations

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Applied Mathematics 2016年第16期7卷 1943-1970页

作者： dimplekumar Chalishajar Austin States Brad Lipscomb Department of Applied Mathematics Virginia Military Institute (VMI) Lexington USA

This paper discusses the mathematical modeling for the mechanics of solid using the distribution theory of Schwartz to the beam bending differential Equations. This problem is solved by the use of generalized functions, among which is the well known Dirac delta function. The governing differential Equation is Euler-Bernoulli beams with jump discontinuities on displacements and rotations. Also, the governing differential Equations of a Timoshenko beam with jump discontinuities in slope, deflection, flexural stiffness, and shear stiffness are obtained in the space of generalized functions. The operator of one of the governing differential Equations changes so that for both Equations the Dirac Delta function and its first distributional derivative appear in the new force terms as we present the same in a Euler-Bernoulli beam. Examples are provided to illustrate the abstract theory. This research is useful to Mechanical Engineering, Ocean Engineering, Civil Engineering, and Aerospace Engineering.

关键词： Mechanics of Solids Discontinuities in a Beam Bending Differential Equations Generalized Functions Jump Discontinuities

Trajectory Controllability of Nonlinear Integro-Differential System—An Analytical and a Numerical Estimations

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Applied Mathematics 2012年第11期3卷 1729-1738页

作者： dimplekumar Chalishajar Heena Chalishajar John David Mallory Hall Virginia Military Institute Lexington USA Roop Hall James Madison University Harrisonburg USA

A stronger concept of complete (exact) controllability which we call Trajectory Controllability is introduced in this paper. We study the Trajectory Controllability of an abstract nonlinear integro-differential system in the finite and infinite dimensional space setting. We will then discuss how approximations to these problems can be found computationally using finite difference methods and optimization. Examples will be presented in one, two and three dimensions.

关键词： Trajectory Controllability Monotone Operator Theory Set Valued Function Lipschitz Continuity Finite Difference Optimization

Review Study of Detection of Diabetes Models through Delay Differential Equations

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Applied Mathematics 2016年第10期7卷 1087-1102页

作者： dimplekumar Chalishajar David H. Geary Geoffrey Cox Department of Applied Mathematics Virginia Military Institute Lexington VA USA

Mathematical models based on advanced differential equations are utilized to analyze the glucose-insulin regulatory system, and how it affects the detection of Type I and Type II diabetes. In this paper, we have incorporated several models of prominent mathematicians in this field of work. Three of these models are single time delays, where either there is a time delay of how long it takes insulin produced by the pancreas to take effect, or a delay in the glucose production after the insulin has taken effect on the body. Three other models are two-time delay models, and based on the specific models, the time delay takes place in some sort of insulin production delay or glucose production delay. The intent of this paper is to use these multiple delays to analyze the glucose-insulin regulatory system, and how if it is not properly working at any point, the high risk of diabetes becomes a reality.

关键词： Delay Differential Equations MATLAB Diabetes Insulin-Glucose Model

Controllability of Neutral Impulsive Differential Inclusions with Non-Local Conditions

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Applied Mathematics 2011年第12期2卷 1486-1496页

作者： dimplekumar N. Chalishajar Falguni S. Acharya Department of Mathematics and Computer Science Virginia Military Institute (VMI) Department of Applied Sciences Humanities Institute of Technology and Management Universe

In this short article, we have studied the controllability result for neutral impulsive differential inclusions with nonlocal conditions by using the fixed point theorem for condensing multi-valued map due to Martelli... 详细信息

关键词： Controllability Neutral Impulsive Differential Inclusions Spatial Partial Derivative Martelli Fixed Point Theorem