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Some Exact Solutions of Generalized Jeffrey Fluid Using n-transform

American Journal of Computational Mathematics 2017年第4期7卷 402-412页

作者： Amir Khan Gul Zaman Saeed Ahmad M. Ikhlaq Chohan Department of Mathematics and Statistics University of Swat Swat Pakistan Department of Mathematics University of Malakand Lower Dir Pakistan Department of Business Administration and Accounting Buraimi University College Al-Buraimi Oman

In this paper, we presents some new exact solutions corresponding to three unsteady flow problems of a generalized Jeffrey fluid produced by a flat plate between two side walls perpendicular to the plate. The fractional calculus approach is used in the governing equations. The exact solutions are established by means of the Fourier sine transform and n-transform. The series solutions of velocity field and associated shear stress in terms of Fox H-function, satisfying all imposed initial and boundary conditions, have been obtained. The similar solutions for ordinary Jeffrey fluid, performing the same motion, appear as limiting case of the solutions are also obtained. Also, the obtained results are analyzed graphically through various pertinent parameters.

关键词： Generalized Jeffrey Fluid Fractional Derivatives Fox H-Functions n-transform

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Solutions of nabla Fractional Difference Equations Using n-transforms

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Communications in Mathematics and Statistics 2014年第1期2卷 1-16页

作者： J.Jagan Mohan G.V.S.R.Deekshitulu Department of Mathematics Birla Institute of Technology and Science PilaniHyderabad CampusHyderabad 500078Andhra PradeshIndia Department of Mathematics JNTU KakinadaKakinada 533003Andhra PradeshIndia

In the present paper,we present some important properties of n-transform,which is the Laplace transform for the nabla derivative on the time scale of integers(Bohner and Peterson in Dynamic equations on time scales,Birkhauser,Boston,2001;Advances in dynamic equations on time scales,Birkhauser,Boston,2002).We obtain the n-transform of nabla fractional sums and differences and then apply this transform to solve some nabla fractional difference equations with initial value ***,usingn-transforms,we prove that discrete Mittag-Leffler function is the eigen function of Caputo type nabla fractional difference operator∇α.

关键词： Fractional difference Caputo type Exponential order n-transform Discrete Mittag-Leffler function

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Controllability and observability of linear nabla fractional order systems

Controllability and observability of linear nabla fractional...

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第37届中国控制会议

作者： Yiheng Wei Yuxin Gao Da-Yan Liu Yong Wang Department of Automation University of Science and Technology of China Juris Master Center University of Science and Technology of China InSA Centre Val de Loire Université d'Orléans

This paper focuses on the controllability and observability properties of linear nabla discrete time fractional order systems. necessary and sufficient conditions are carefully established for these fundamental structural properties. The results are then restated in three different forms, which happily prove to be similar as the continuous time case. An illustrative example is presented to illustrate the theoretical results.

关键词： Fractional order systems nabla discrete systems Controllability Observability n-transform

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Design and analysis of the sine and cosine functions in fractional order case

Design and analysis of the sine and cosine functions in frac...

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第37届中国控制会议

作者： Yuxin Gao Yiheng Wei Juris Master Center University of Science and Technology of China Department of Automation University of Science and Technology of China

This paper systematically investigates the trigonometric functions from the exponential function point of view. After recalling the classical exponential function, the Mittag-Leffler function is introduced as a generalization. Then, the cosine function and sine function are extended to the fractional order case. With the introduction of nabla discrete time case, a corresponding exponential function is defined. By using the n-transform, the discrete time cosine function and sine function are designed and analyzed both in the integer order and the fractional order cases. To solve the periodic oscillation problem, the poles are specially chosen and laid in the marginal position. Illustrative examples are provided to validate the elaborated results.

关键词： Fractional order systems nabla discrete systems Controllability Observability n-transform

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